It isn't a reminder of his brilliant career with the Pumas, which lasted for almost 20 years and made him one of the most famous of Argentine sportsmen. Even now, aged 61, the former first five-eighths is one of the best known rugby names in his country because of the flair, finesse and goalkicking talent that he packed into his 58 tests between 1971-90.
No, it is a framed photo of a meeting he had with Pope John Paul II during the Pope's visit to South Africa when he was Argentina's ambassador to the republic. Between them is President Nelson Mandela, who was explaining to the Pope, says Porta now - with a tinge of embarrassment in his voice - what a great athlete the Argentine once was.
How he got to be in that position as Argentina's ambassador to South Africa from 1991-95 when he became close to the man who would defuse the ticking timebomb of the troubled country sounds like the stuff of fantasy and Porta, though he must have told the story many times, still seems amazed by it.
Porta left the role straight after the Rugby World Cup there, a tournament which helped unite a nation thanks to the Springboks' victory and the fact that Mandela famously wore the green jersey with the gold collar - one that had been hated by the black and coloured populations as a symbol of the apartheid era - to present the trophy to captain Francois Pienaar.
"It's quite a story," he says of his life since retiring from rugby at the age of 39. It's not hard to agree.
After only a short time running the family business - a kitchen and bathroom wholesalers - he had a message from his wife to ring Argentina's president.
Once he had recovered from his shock he arranged a meeting and was told: "You know, I want to re-establish ties with South Africa.
"I said to him I think it's a good idea because we are very close to South Africa. If you fly straight from Buenos Aires to Cape Town it is only seven and a half hours of flying. I said there are lot of opportunities and it would be good for both countries. He said:'I think you should be the ambassador to South Africa.' I said,'what an honour, but I can't give you an answer now'.
He said to me:'You do realise the opportunity that I'm giving to you', and I said'to be honest, no'."
Porta was given four days to think on it. After much thought he decided he would take the job and rang the president. Before he could say anything, he was asked: "Ambassador, how are you?"
So, out of nothing and with no experience in diplomacy, Porta travelled with his wife and two young children to Pretoria, assembled a foreign embassy, and watched first-hand as history unfolded.
On moving back to Buenos Aires, Porta became the Minister of Sport. He says the four years in the job were difficult, but is proud of what he achieved and the fact that he is still liked by a public which has a natural distrust of politicians. In a cafe near his office after our talk, a man introduces himself to Porta, and hearing us speaking in English turns and says: "The greatest player ever, the greatest."
Porta has the natural good humour and pleasant demeanour of a diplomat, but in talking to him his strong will and refusal to compromise on his ideals becomes clear.
Cynics could say that having come from an relatively wealthy family, rather than the more modest roots of his countryman Diego Maradona, he could afford to have principles, but he has worked hard for his rewards.
He is also a qualified architect and when he is not working in the family business he spends time on the Laureas Foundation, a charity he helped set up which provides for children with the help of sport.
Porta says the amateur game was the making of him and hopes Argentina's clubs are not forced to go professional now the country has joined New Zealand, Australia and South Africa in the Rugby Championship.
The game has already become too regimented by the use of technology and analysis, he says. Players don't play with the flair of his day because of a lack of space on the field and the fact they must stick to a game plan.
There is little room for imagination on the playing field, but he still loves the game and is thankful for what it has provided him.
"Rugby is an expression of a culture. Cultures are different around the world. So what I would say is very important is that the people who are running the game internationally respect the different cultures. I don't think you can apply the same recipe in Argentina, in New Zealand, or in Samoa.
"It's very important for us to have the Rugby Championship in Argentina, but it's also very important to keep the culture of our [amateur] clubs.
"Our professional players are special, but they were grown by amateur clubs. They were grown by people who had given their time for free for them to play rugby. It's difficult to know what's going to happen. On one side it's great - you have seen the Pumas play their first game of the season and you will see on Saturday [Sunday NZ time] a Pumas team play differently because the team is developing all the time."
On the messages relayed to players during tests and the intense analysis, Porta asks: "What is the challenge here? And what are we learning here? Are we learning to think for ourselves under pressure? Because they are the things we are going to use for our lives."
Asked if he looked back on his life and wondered at the different turns it had taken, Porta says: "I am 61 years now, if I don't look back now, then when?
"Yes, I look back. The possibilities that rugby gave to me are immense. Through rugby I understand what sharing is all about because I am an only son. I was very spoiled by my parents. Through rugby and the club I met my wife, I had my family, I learned the things that are ruling this company now. Through rugby I helped re-establish the relationship with South Africa - on the other hand to be an ambassador is common sense.
"I have one regret. I didn't go to the Rugby World Cup in New Zealand [due to work commitments]. When I came back from this short trip to New Zealand [to watch Pumas play in Wellington recently] I said to my wife it was a mistake not to go there because the love and the way that you care about me there was amazing. It's good for your soul. You think,'I'm 61 and people still remember'.
"There was a young boy who came to see me [in Wellington] and he said, Mr Porta, I'm Mr Porter. I said'I'm pleased to meet you, what is your first name?' And he said'Hugo'. My father named me Hugo because of you."
• Patrick McKendry flew to Argentina courtesy of LAN Airlines (www.lan.com).
