Nelsen scored his first goal for Spurs in a 3-1 quarterfinal win over Bolton to book a semifinal clash with Chelsea at Wembley.
Spurs manager Harry Redknapp was effusive in his praise for the defender after the game and hinted a new deal was on the horizon.
"Ryan Nelsen is a fantastic professional," he said. "I can't believe I picked him up on a free transfer.
"I had been chasing him for years and he's only on a six-month contract, so we'll have to give him a new one at the end of the season."
Nelsen signed for Spurs after leaving Blackburn, following 172 matches in eight seasons, on deadline day in the January transfer window. The 34-year-old has since made five appearances for the club, while three starts at the heart of the Tottenham defence in the FA Cup have helped his side reach the last four of the oldest football competition in the world.
"He's worth his weight in gold just to have him around the place - football clubs are built on great characters like him," Redknapp added.
Nelsen had been thought to be eying a move back to the United States, where he started his career with DC United in the MLS, but that will be on the backburner if Redknapp is keen to retain his services for next season.
After yesterday's win - which was a replay of the tie that was abandoned when Bolton midfielder Fabrice Muamba went into cardiac arrest - Tottenham are now two wins away from claiming their ninth FA Cup.
Nelsen was twice knocked out of the semifinals of the competition when at Blackburn, and if Spurs manage to advance past Chelsea he would become the first New Zealander to play in an FA Cup final.
