Roma have reportedly offered €7.5m for co-ownership of Cagliari defender Davide Astori, also a target for Milan.
The centre-back has been linked with both these clubs along with Southampton, Sunderland and Everton.
He had been on the verge of a €13m move to Napoli earlier this month, but the deal collapsed when Rafa Benitez pulled the plug.
According to Sky Sport Italia, Roma made the new and improved offer for half of Astori’s contract on Friday night.
The bid is worth €7.5m for co-ownership of the player, leaving half his registration in Cagliari’s hands.
However, Cagliari President Massimo Cellino has repeatedly stated the club will not be selling any of its big stars this summer.