Roma sporting director Monchi has said the club allowed goalkeeper Alisson to speak to Liverpool after receiving "a significant offer," with the player undergoing a medical on Merseyside.
Speaking at the official unveiling of Justin Kluivert at Roma, Monchi said the club had reached agreement with Liverpool after evaluating the bid.
"The player's there undergoing a medical and, if he passes that, the deal could go through," he said.
"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 to make us an even bigger club."
Alisson is set to move to the Premier League for a world-record fee for a goalkeeper after keeping 17 clean sheets in 37 Serie A appearances last season.
Liverpool were the only club to score against him in the Champions League at the Stadio Olimpico last season, striking twice in a 4-2 semifinal defeat but progressing to the final.
Alisson's unbeaten record against Chelsea, Atletico Madrid and Barcelona saw him go from backup to Wojciech Szczesny in 2016-17 to one of the world's most sought-after keepers.