If a meeting does happen, it will almost certainly not be this month.
Mayor Jules Radich issued a statement saying Mr Robertson’s office had cited "diary pressures" as getting in the way and it suggested the Dunedin City Council should continue to work with Minister of Health Dr Ayesha Verrall.
The city council has been running a campaign against cuts to the design of the new hospital.
The Government has endured a sustained backlash in Otago since it announced late last year escalating costs would be dealt with by boosting the project budget by $110 million and achieving design "savings" of $90 million.
Both the city council and the Otago Daily Times launched campaigns urging the Government to build a hospital that will be fit to meet the region’s future needs.
Labour Party MPs have sometimes been dismissive of concerns about the new hospital, but Dr Verrall visited Dunedin in February on her second day as health minister.
Her office confirmed last week Mr Radich sought a follow-up meeting.
Mr Robertson’s office said it told TVNZ a few weeks ago he was working closely with Dr Verrall and he intended to meet the mayor in May.
Mr Radich said he was disappointed Mr Robertson was "currently too busy" for a meeting.
"I have no expectation of meeting the Minister of Finance in April, but I have high hopes of having a chat in May," Mr Radich said.
"Southern residents are right to be concerned and I will do whatever I can to represent our communities and have our voices heard in Wellington."
The Government has presented much of the proposed adjustment as efficiencies.
Mr Radich said clinicians were not convinced a "cut-back" hospital would be sufficient.
"To be honest, I think the Minister of Health will say that she simply doesn’t have the budget.
"If that is indeed her final answer, I’ll be heading down the hall to the Minister of Finance to ask how he is justifying a cut-back hospital that will be less than fit for purpose."
