Salah's hopes of leading Egypt to victory in the Africa Cup of Nations were dashed by his former teammate Sadio Mane.
Hamann's comments come in the wake of Egypt's exit from the Africa Cup of Nations semi-finals after a loss to Senegal, which ended Salah's hopes of winning the continental title.
Hamann said in comments published by Liverpool.com regarding Salah's decision to sign with the English team despite his contract having expired: "He could have gone to Saudi Arabia last season, but he didn't."
e added: "I'm not sure if he wants to go there, but if you asked me today, his departure would be the best solution. It would probably be in his best interest and the best interest of the team."
In contrast, Hamann stressed that competition within the team should be the primary criterion, explaining that the presence of outstanding attacking players forces any player to accept competition for his place regardless of his history or name.
He raised a question about Salah's willingness to sit on the bench if the coaching staff felt that someone else was technically better in some major matches.
He concluded: "I see no problem with Salah and Wirtz working together. It's true that Salah has struggled to score from open play since last Christmas, but the question is, to what extent is Salah still able to influence matches? He is 32 or 33 years old, and for attacking players, six months can make a huge difference."
Salah is scheduled to return to Liverpool next week after playing in the third-place playoff on Saturday evening, and therefore will miss the Burnley game.
Salah could return to action for Liverpool against Marseille in the Champions League before the Reds meet Bournemouth next weekend.
