Selling Alisson to Liverpool does not show "a lack of ambition", says Roma's director of football Monchi, who admits the transfer of the Brazilian is "tough" for fans to take.
The Reds have agreed a fee of about £66.8m for the goalkeeper.
Roma say Alisson is now in Liverpool and "negotiations are advanced".
"When a very substantial offer comes in you have to consider it," said Monchi. "We weighed up the pros and cons and decided to speak to Liverpool."
"Selling Alisson would not show a lack of ambition. For me, ambition is about doing the right thing after thinking everything through."
Liverpool's bid, which is 70m euros, would overtake the current record for a keeper - 53m euros paid by Juventus to Parma for Gianluigi Buffon in 2001.
Alisson, 25, has been at Roma for two years, and played 37 Serie A games last season, after starting his career at Brazilian side Internacional.
Roma's high profile signings this summer include midfielder Javier Pastore from Paris St-Germain for £21.8m and winger Justin Kluivert from Ajax for £15.16m.
Belgium midfielder Radja Nainggolan was sold to Serie A rivals Inter Milan.
Monchi added: "I understand the fans' view. I want them to know we're working to build a stronger team. Some people never thought we'd be able to sign Kluivert. The same goes for Pastore. Perhaps today is tough for some fans, but we've brought in top players.
"I came here to build a strong team, not just for one year but for many years to come - and I'm 100% sure that will be the case."