The Brazilian is said to have been approached by a Saudi club in the last few months.
The Saudi Pro League wants to bring in more top talents this off-season, with his teammate Mohamed Salah also a major target.
Speaking on his Youtube channel, transfer expert Fabrizio Romano said: In the last few days we heard rumors on Alisson and proposals from Saudi.
I'm told that there was some approaches around March, April for Alisson, trying to understand the situation around the Brazilian goalkeeper.
The answer I got, as of now, and never say never in the market, but as of now, and of May, is that there was some approach, but Alisson is expected to stay at Liverpool."
He added: Liverpool are not planning to change the goalkeeper, they are very happy with Alisson, Alisson is very happy at Liverpool. He's not desperate to change, he's not looking for money.
And so, at the moment, there is no expectation for Alisson to leave Liverpool in the summer transfer window for Saudi."