The 'Reds' travel to Yorkshire this weekend as the Premier League as the English top league returns after the international break.
Salah, last season's Premier League top scorer, has been struggling with a hamstring injury picked up on international duty with Egypt, while Mane had an issue with his hand, which he suffered playing for Senegal.
The two attacker have contributed a total of nine goals and assists to their team in the league this season and it had been feared that the two integral attackers would miss the game this weekend.
However Klopp has not ruled out either of the members of his famous front three being available for the clash.
"We had yesterday's session and a few of the boys trained, we'll have to see how they react," said Klopp ahead of the game.