"The player's there undergoing a medical and, if he passes that, the deal could go through," Monchi told reporters.
"It's hard when you're a sporting director. We received a significant offer for Alisson and we evaluated it.
"In the end, we took a decision and, speaking with Liverpool, we reached an agreement. It's not that we lack ambition. We've only sold two players and we've signed 10, and we're going to continue looking for players."
Alisson kept 17 clean sheets in 37 Serie A appearances for Roma last season and helped the club reach the Champions League semi-finals, where they were knocked out by Liverpool.
He started all five games for Brazil at the World Cup in Russia where they bowed out with a quarter-final defeat by Belgium.
The goalkeeping position has been problematic for Liverpool under manager Juergen Klopp, with Loris Karius and Simon Mignolet struggling to hold down their first-team spots last season.
(Reporting by Hardik Vyas in Bengaluru; Editing by Ian Chadband)
