Roma are not in any rush to replace Alisson following his move to Liverpool, sporting director Monchi has said.
Alisson's move for an initial €62.5 million -- a world record for a goalkeeper -- went through on Thursday.
Monchi said Copenhagen's Sweden international goalkeeper Robin Olsen was a candidate but added that he would not be hurried into any signing.
"He's an option, but he's not the only one," he told a news conference. "We're working calmly and without rushing things.
"The best thing to do is find a deal with the best economic conditions for the club rather than make a decision under pressure as a result of the sale of Alisson."
Monchi said he could understand Roma fans being unhappy at seeing Alisson leave, but said he believed it was the right business decision.
"I don't think there's a sporting director in the world that understands the fans' point of view more than I do," he said. "At times, I'm too much of a fan. But I have to take decisions based on what's best for the club.
"Perhaps some of the fans are angry today, but we know that all the fans are happy when Roma win. That's my job -- find a way to build the strongest team possible and make the fans happy."
He praised Alisson and wished him well at Anfield, adding: "I only have words of thanks for Alisson -- I never felt pressured by him to let him go.
"If he accepted the Liverpool offer, it's because he was happy with it. He's behaved flawlessly with me. As a sporting director, you need to try and understand what's going to happen as quickly as possible.
"When you start hearing rumours about Real Madrid, Chelsea and Liverpool you can either pretend that nothing's going on and plough on as normal, or you can accept that something could happen and work to find the best solution for the club."
He repeated his call to the fans to be patient and trust that he is doing all he can to deliver a trophy to Roma.
"A sporting director comes in from Spain and a Roma fan that hasn't enjoyed success in ages could well just tell him to go back to Seville," he said.
"I've been here for 14 months and I can't do anything about the fact that Roma haven't won anything in years. I need time -- I know it doesn't exist, but we need it.
"We got to the Champions League semifinals, so I think we deserve a bit of faith. I know everyone is tired of talk and just wants to win. I always front up and my confidence is still at 100 percent. If I've not won anything in a few years, I'll book a flight and leave."