A report in the Italian press earlier this week suggested that Roma have already turned down a £35m bid from domestic rivals Napoli, meanwhile, which is said to be less than half of what the Giallorossi value him at.
According to Monchi, though, Roma are not prepared to let Alisson leave and he has reiterated that the Brazil international is happy at the Stadio Olimpico.
"We are not afraid of losing Alisson. He is happy to be here with us and we are happy with him," he told Mediaset Premium. "What you read in the papers isn't always true. We don't know of any offer and certainly haven't received any proposal.
"I speak to Alisson every week, he is happy and wants to do important things here at Roma."
Speaking earlier this week, Alisson admitted to being flattered by the links to Liverpool and Real Madrid.