Salah was forced out of the FA Cup final against Chelsea in the first half with a groin injury.
Van Dijk had to replaced before extra-time due to a knee problem, before the Reds went on to win the trophy 6-5 on penalties.
Defeat for the Reds at St Mary's Stadium would see Man City crowned champions but manager Jurgen Klopp is unlikely to take any risks with the Champions League final to come at the end of the month.
Klopp said at a press conference: "This process is not finished yet. We played 120 minutes only two days ago.
"The boys only arrived today (Monday) and we have to make a lot of decisions.
"But what I can promise, definitely, is we will line up to try to win the game at Southampton. We have a job to do and we have to see who is able to help."
Fabinho, who missed the cup final with a thigh injury, is not yet ready to return, but defender Andy Robertson should be available after suffering cramp on Saturday.
After Manchester City's draw at West Ham on Sunday, Liverpool can move back within a point of the leaders heading into the final day if they beat Southampton.
It would keep their hopes of the quadruple alive with two trophies already in the cabinet.
Klopp said: "I am really looking forward to the game tomorrow. Is it a big chance? I wouldn't say so because I don't know when City last dropped points two games in a row.
"I don't expect City to drop points but that has no influence on our game tomorrow. In an ideal world we'll go into the last match one point behind."