The Egyptian striker was on target for the Reds as they beat Ipswich Town 2-0 away from home.
The Reds were not at their fluid best, but did more than enough to earn three points on opening weekend.
Salah, who is now 32, is tipped to keep going by teammate Andy Robertson.
“Every year he comes back in even better shape than he was the season before,” said the Scotland captain.
“He was one of the players who had a longer summer which was hugely beneficial to him. He managed to get a full pre-season under his belt and looks fit and sharp.
“He was excellent, especially in the second half when he carried us over the line.
“Mo looks after his body exceptionally well. He's a model professional and someone everyone looks up to. He leaves no stone unturned and that's why he's still in incredible shape.
“Long may that continue. If our main man is playing like that then it's going to help the team.”