The Egypt international, who joined for what was then a club-record fee of an initial €42 million last June, has scored 28 goals in all competitions in 2017-18.
Salah's latest strikes, including a sublime solo effort, came in the 2-2 draw with Tottenham last Sunday, which took him to 21 league goals in 25 appearances – already six more than he managed in Serie A last season.
"I've got to hold my hands up and say I didn't anticipate it," the former Scotland international, who helped Liverpool win a treble of EFL Cup, FA Cup and UEFA Cup in 2001, told Omnisport. "I thought he was an outstanding player but I've got to say, he's gone way up in my estimation. He's a stunning player.
"Not only his goal-scoring efforts, his skill and technique, but also, he's robust. He works his socks off for the team. He's very much a team player, but he's been outstanding."
John Aldridge, a league champion and FA Cup winner in his two years at Anfield from 1987 to 1989, says Salah's goalscoring form has been remarkable for a winger.
"If we're going to finish top four and hopefully second or third then we need him to keep on going in the manner which he is," he told Omnisport. "You know, it's just ridiculous to see a winger score that many goals and fighting against Harry Kane of all people for the Golden Boot. Sensational. Brilliant."
Liverpool's new record signing, Virgil van Dijk, has endured a more difficult start to life at the club after moving from Southampton for a reported £75m fee in January.
The centre-back conceded a last-minute penalty against Spurs that allowed Harry Kane to equalise and was on the losing end on his league debut against Swansea City.
But McAllister, who was impressed by Van Dijk during his time at Celtic, is confident he will prove to be an excellent addition to Jurgen Klopp's squad.
"I've seen a lot of Virgil van Dijk. I worked in Scotland for a little bit when he signed for Celtic," he said. "I was impressed by him then and people were sort of flippantly saying that he's playing in a league that's too easy for Celtic, which is true, but you can see the quality.
"I think we've signed a quality player. He'll turn out to be a fantastic signing."
Aldridge added: "Van Dijk is a very, very good centre half and he'll go a long way to helping us get, or trying to achieve what we want and our goals for the coming season."
Chelsea's dip in form has allowed Liverpool to move one point above them to third in the table, adding a positive spin to a recent run in which they followed a 1-0 loss to Swansea with an FA Cup exit at the hands of West Brom.
But McAllister believes they can have a very positive second half of the season and is quietly confident about their prospects in Europe, with a last-16 tie with Porto in the Champions League on the horizon.
"I don't think Liverpool have been doing a great deal wrong," he said. "The two little blips against Swansea and West Brom in the cup... I thought the game against Spurs it was an excellent game. I thought it was two outstanding football teams with loads of good footballers on show so it's a case of just getting that run again to push on and push to make it as difficult as they can to the teams above us."
He added on the Porto tie: "I've got to say, before the draw for the last 16 was made, I don't think many teams wanted to play Liverpool over two games.
"When we actually click and say yes, I think we're a difficult proposition and we're capable of beating anybody over a two-legged affair. So, I'm very hopefully and optimistic to continue the good run in Europe."