Premier League side Liverpool are thought to be among the clubs harbouring a serious interest in the Brazil international, particularly given the inconsistent performances of Loris Karius and Simon Mignolet.
However, in an attempt to fend off said interest, it is believed that Roma have offered their star a bumper new contract, with an £80m release clause.
Italian publication 'Calciomercato' reports that the 25-year-old has demanded his wages be increased from £1.35 to £4.45m in order to get him to agree to the new deal.
Alisson is a key player for Roma, hence their desire to tie him down long-term, though the club knows that a big money offer could force their hand, owing to their precarious Financial Fair Play position.