Roma sporting director Monchi is willing to consider offers for Alisson, but revealed the club is yet to receive a bid for the goalkeeper.
Brazil international Alisson has been linked with the likes of Liverpool, Chelsea and Real Madrid after shining for Roma in their run to the Champions League semi-finals.
But despite speculation he could be tempted away from the Italian capital, Monchi says Alisson is staying put as things stand.
"He has the same chance of staying as all the other players we have not received any offers for," Monchi told reporters.
"If one arrives, we will study it and make a decision. We are working out when he will return to training after his post-World Cup holiday; ready to do even better than he did last season for us."
Roma have had a busy transfer window, making 10 signings including Ivan Marcano, Justin Kluivert and Javier Pastore.
But the Serie A side have been linked with further arrivals, Ajax's Morocco international Hakim Ziyech and Sassuolo forward Domenico Berardi among their reported targets.
"As I said on Saturday, we are always watching the transfer market," Monchi added. "Roma is a big club, and big clubs always need to have an eye on the market up until it closes.
"We still have 40 days, so talking about Ziyech or Berardi is reductive. We are following a lot of situations. We have started the pre-season. When you are building a side you always think you are doing well, but this is the time to understand how you can continue to improve.
"Hard work is always the most important thing, I don't know any other way to achieve success. We have chosen a risky strategy: to build the squad as quickly as possible, to get down to work immediately.
"There is a gap we need to overcome to those who finished ahead of us, we have to work to close it as quickly as we can."