The 23-year-old midfielder was born and raised in Rome as a product of the Roma youth academy and never disguised his desperation to return, especially when negotiations reached an advanced stage last summer.
However, those talks broke down over the €30m asking price and it only increased after another positive season for the Italy international.
“I hear that many Italian sides have approached Frattesi, but not by talking to us,” Carnevali told DAZN ahead of this evening’s final Serie A match of the season against Fiorentina.
“As far as we are concerned, the only market for Frattesi is the Premier League and we had some contacts.”
Frattesi signed a new contract in March 2022 that holds him to the Mapei Stadium side until June 2026.
He has four senior caps for Italy and this season has contributed seven goals in 36 Serie A appearances for Sassuolo.
Arsenal had been very close to agreeing terms with Sassuolo for Frattesi last year, but the player was determined to push through the move to his hometown club Roma instead.
It is possible they are again the front-runners from the Premier League for the midfielder.