The 30-year-old Argentina international midfielder has been in impressive form for River since returning to the club earlier this year from Real Zaragoza.
Ponzio has split the last nine years of his career between River and Zaragoza, spending two three-year stints in Spain with another two-year period back at the Estadio Monumental sandwiched in between.
Spurs are believed to have watched Ponzio in the derby clash with Boca in which he scored the equaliser in the 2-2 clash.
"I knew that some people came to watch me in the match against Boca and I think in another game too," said Ponzio.
"Nobody spoke with me about a possible transfer or real interest. Anyway, regarding my future, I am very comfortable where I am and I feel respect. I would like to take advantage of this moment."
Asked specifically about a possible move to England with Tottenham, he said: "What comes for my career from now on will be analysed. At my age I have to analyse everything with my family.
"It's not a year yet since I came back from Spain. Therefore, if an offer arrives, River and me will have to analyse it.
"I am at a good personal moment and I have to keep on going on in that way. I would like to have the chance to play for the national team again, so I have to keep on doing well at River."