The trio, who were all knocked out of the World Cup in the group stage, were given extended time off following their participation in Russian Federation.
Salah has had some break from football in the past couple of weeks after having a very long season with Liverpool after reaching the Champions League final as well as competing with Egypt in the 2018 World Cup.
Both players were given extra time off following their World Cup involvement with their respective countries, but returned to Melwood on Friday ahead of the club's United States tour.
Liverpool also announced that Mane will near the number 10 shirt next season, which was previously worn by Brazilian playmaker Philippe Countinho before he left for Barcelona in January.
Liverpool will play three friendly matches at the International Cup of Champions against Borussia Dortmund on Sunday, Manchester City on Thursday and Manchester United on Saturday.
Other club legends have also donned the jersey before, including John Barnes, Michael Owen and Jan Molby.
New signing Naby Keita has been allocated the number eight shirt, famously worn by Steven Gerrard, after completing his transfer to the Reds from RB Leipzig.