The Italy international is one of the Giallorossi’s prime transfer targets this summer.
And Corriere dello Sport report Roma will speak to Sassuolo again on Wednesday as they look to agree a deal below the €30 million asking price.
At present, the report adds, Roma are not willing to part with more than half that amount in cash.
Frattesi, 22, made his Sassuolo debut in 2017 and, after loan spells at Ascoli, Empoli and Monza, enjoyed a breakthrough 2021-22 campaign in which he became an integral part of the Neroverdi squad and made his Italy debut in June this year.
Roma have also been heavily linked with Frattesi’s Sassuolo team-mate Maxime Lopez, who recently hinted he could be set to leave the club this summer.