Giacomo Bonaventura was offered to Lazio, according to Il Messaggero newspaper, but the Biancocelesti are unconvinced.
The midfielder turns 31 next week and is a free agent after his contract ran down, ending a decade with Milan.
He has been linked with several clubs in Serie A, including Hellas Verona, Atalanta, Benevento and Crotone.
Il Messaggero newspaper claims his agent Mino Raiola also offered him to Lazio.
However, the Champions League qualifiers are concerned at bringing in someone with such a high salary and recent injury concerns.
Bonaventura scored four goals and provided six assists in 34 competitive games for the Rossoneri this season.
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