The Italian footballing legend has fallen out of favour at Roma, with new head coach Luciano Spalletti dropping him from recent matchday squads.
At the age of 39, Totti is nowhere near his previous level of ability, but Claudio Ranieri believes he can still do a job for Leicester, and the Italian boss wants to convince Totti to move to the Foxes for one season in the Premier League.
Totti is considering his future with Roma following the fall-out with Spalletti, and he will make a decision on whether to stay or leave in June.
There have been suggestions Totti could retire immediately after leaving Roma, as they are the only club he has played for, but Ranieri is a big fan of the striker he coached back between 2009 and 2011.
Totti will be available on a free transfer if he does move this summer, as his contract with the Giallorossi expires at the end of this season.
Totti made his debut for Roma in 1993, and has gone on to score 293 goals in 721 games for his hometown club.