Pulis was sacked as Baggies boss on Monday following a nightmare run of only two wins from their last 21 Premier League games, with the Welshman leaving the club just one point above the relegation zone.
Pardew, who has been out of a job since his departure from Crystal Palace in 2016, is the current odds-on favourite to take over in The Hawthorns hotseat.
Ashton played under Pardew during his time at West Ham United, and he insists his former boss would be an ideal choice to lift the gloom and get West Brom firing again.
The former striker, who had tipped Pardew to return to the Hammers before they eventually opted for David Moyes, told Hawksbee and Jacobs: “The whole experience of playing under him as a manager was a positive one
“As a player, having looked at Tony Pulis and from what I’ve heard, the training is hard, there’s a lot of work on the shape and organisation of the team, which is obviously important.
“Under Pardew, you do get that as well, but the training was fun. It was about attacking football, his philosophy is about how can we attack this team and exploit this team.
“The training was great and he was great with the players.
“He gets a bad rap because of what happened at Newcastle and Crystal Palace, and maybe one fault of his is that he gets on too well with the players, so that when things go poorly it’s hard then to get the respect he needs. I’m sure he’s learned from that.”
“From a personal view, I enjoyed playing under him. I enjoyed the style and I think the fans who have watched his teams would say the same.
“He doesn’t lack confidence, I can say that about Alan Pardew, but that rubs off on the players and the way he brings himself into the club and the style of football he brings, it does give everybody a lift.
“If that’s what you’re looking for, for somebody to come in and lift the players and play more attacking football, he’s certainly a manager to look at.”