Pellegrini's future is in doubt due to his €30m release clause.
However, Giampiero Pocetta told Sky Sport Italia: “There's been a lot of talk about him, there have been talks with several teams who have shown us their projects, some of which are very interesting.
“Lorenzo is flattered by all this. Clubs in Italy and abroad wanted him, but he's determined to stay at Roma.
“Totti's words have charged him with responsibility, he's a mature lad and he doesn't shy away from situations like these.
“Beyond that, however, he's convinced of the validity of Roma's project. If he wanted to leave, he would've done so already.
“The release clause was included in his contract because it gave him the opportunity to leave in the event he no longer wanted to stay.
“Pellegrini's desire right now is to stay at Roma. We're also discussing a new contract with the club, even if - as in the case of the clause - we have no urgency in defining certain things."