However Roma chief Monchi spoke to Premium Sport ahead of his side's 1-1 draw with Bologna on Saturday, and was adamant he will not allow the Brazilian goalkeeper to leave Rome.
“He [Alisson] still has room for growth, but I'm a bit tired to talk about his future,” he said.
“They always ask me the same questions, but up to now we have not received any offers. We are not going to sell him.
“We are happy to have him at our club and and we want to take advantage of his work.
“What is his price? I won't say, because I don't intend to sell,” he added.
Earlier this month, Monchi was quoted by Spanish sports newspaper Marca, claiming he is unbothered by rumours surrounding the reported Liverpool target.
“Let us not forget that he is the Brazilian national team’s first choice goalkeeper and he therefore commands a lot of attention. Nobody has asked me about him but these rumours do not bother us.
“The dream of every sporting director is to find talents like Messi and make him sign a lifetime contract. At Roma, we do not have many examples of such players.
“There is only Totti who won the Scudetto and a World Cup, while remaining at the club for 25 years. It is difficult to repeat his success.”
Alisson has enjoyed a fantastic season in Rome, which has attracted plaudits from the wider footballing community. Brazil goalkeeping coach Claudio Taffarel was the latest to be full of praise for the stopper, suggesting he could become the world's best.
“You always have to be ready for when the chance comes along,” Mignolet told Sky Sports.
“That’s the only thing I can do so I try to stay professional in training, try to work as hard as I can, show that I’m ready for whenever the chance happens.
“That’s the only thing you do really, then it is up to the manager or the coach to give you the nod.
“It is never easy of course because I have never in my career spent time on the bench, but it is how it is and the only thing you can do is try to change it but it is never easy.
“I’ve had a few conversations with the manager already and we have spoken about numerous things.
“I’m always open and he’s always open, you know how he is, but at this time it is not the time and place to do that.”