The pair are waiting to settle on new contract talks with the club.
Fabiani said: "We offered Felipe Anderson, an exemplary professional, a five-year contract.
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Zaccagni's contract runs out in 2025, and we'll try to match his needs. He has given a lot to Lazio, but to extend a contract, you need the will of the counterpart, too.
"If he receives a 50m offer, we can do nothing."