Roma's sporting director Monchi has stressed selling Alisson "would not show a lack of ambition" as he confirmed the player was in Liverpool on Thursday.
Press Association Sport understands Liverpool have agreed to meet Roma's valuation of 75 million euros (approximately £67m) for Alisson, a figure which would make the 25-year-old Brazil international the most expensive goalkeeper in history.
On Wednesday, Italian website Forza Roma, which is affiliated to newspaper La Gazzetta Dello Sport, published a video which it said showed Alisson at Rome's Ciampino airport. It said he was preparing to board a private jet to Manchester and was on his way to Liverpool for a medical.
Speaking on Thursday at a press conference to present Roma's summer signing Justin Kluivert, Monchi was quoted on the Serie A club's official twitter feed as saying: "We haven't finalised anything yet (with Alisson).
"But it is true that the negotiations are advanced and he's over in Liverpool now."
Monchi, who took up his post at Roma in 2017, added: "When a very substantial offer comes in, you have to consider it.
"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.
"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.
"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 (fellow summer signing Javier) Pastore.
"Perhaps today is tough for some fans, but we've brought in top players."