Nesta may miss rest of season
"In the next few days we'll consider whether I should have an operation or not," he told reporters after leaving a clinic in Rome.
"I don't know if I'll miss the rest of the season. Even if I have to have surgery I could return for the end of the championship."
The 33-year-old, who has endured a series of injury torments, turned down the chance to come out of international retirement and play for Italy earlier this month.
He was badly missed on Tuesday when Milan lost 4-0 at Manchester United to go out of the Champions League last 16 and the Rossoneri will struggle to fill the void in the Serie A run-in.
Second-placed Milan, four points behind leaders Inter with 11 games left, also have injuries to defenders Luca Antonini, Daniele Bonera and Oguchi Onyewu ahead of Sunday's home game with Chievo.
Leonardo's side have not won the scudetto since 2004.