The winger, who arrived from Juventus in the summer, is in line to make his debut in the coming games.
Chiesa, who starred at Euro 2024 with Italy, may play against Italian giants AC Milan in the Champions League in midweek.
Alisson told reporters: “I don’t need to give you any introduction to Federico Chiesa because he is a wonderful football player, you perfectly know him much better than we do. In the past years he has given proof of his quality.
“He got injured, he had some ups and downs, he had some bad periods, but the way he landed in Liverpool was extremely positive, to me. He arrived to our squad with a huge smile painted on his face.
“Everybody is enthusiastic about Federico and he is extremely happy about having this chance of playing in our squad. His quality, he shows it every time, every day. We are lucky to count on him, he is a top-level player who can help our team.”