Steven Gerrard has said Andoni Iraola's management style would be an ideal fit for Liverpool but that other managers will also be in contention after the club sacked Arne Slot.
Slot paid the price for Liverpool's disappointing defence of their Premier League title and Iraola has emerged as a clear favourite for the job after his departure from Bournemouth.
When asked if the 43-year-old Spaniard would be the right choice, Liverpool great Gerrard told TNT Sports: "I think potentially, yes. I think he's done a fabulous job at Bournemouth. I think his style would suit Liverpool.
"But let's not beat around the bush. Liverpool Football Club is an attractive job for a lot of elite managers around the world.
"So I don't think he'll be the only name on the table. But because of the link to Bournemouth and the guys that have come from Bournemouth to Liverpool in terms of board level, they will know him very well.
"But then there's other names out there as well that I'm sure will want that Liverpool job. It's a huge job in world football.
"But potentially to answer your question, I think he should be in the conversation, yes."
Fans turned on Slot after a number of poor performances -- the team lost 19 times this season -- and there was some disharmony in the dressing room, with Mohamed Salah the most outspoken.
Gerrard said Slot "did an incredible job in his first year" and would be "remembered forever" after winning the title.
But the former Reds skipper added: "The last 10 games of last season, and for the majority of this season, we haven't looked like Liverpool. The style has been difficult to watch at times.
"It looks disjointed, it looks broken, and when I got the news today, of course, your initial reaction is surprise and shock, but when you analyse it properly, it's probably the right time, in my opinion."
Sources told ESPN that the feeling at the club was that change was inevitable this summer after a turbulent season.
Slot has faced criticism for a perceived lack of intensity and the club is targeting a more attack-minded, aggressive style of play, sources told ESPN.
The decision to sack Slot was a reluctant one given the scale of his achievement in winning the Premier League after replacing Jurgen Klopp.
However, sources told ESPN that officials at the club believe a change of manager gives Liverpool the best chance of success moving forward, with the search for his successor having already begun.
That move to a more intense style of play reflects comments made by Salah in a social media post earlier this month when he called for a return to the "heavy metal football" played under predecessor Klopp.
Liverpool insist the desire for a change of style should not be viewed as a criticism of Slot.
"Liverpool FC can confirm Arne Slot is to depart his role as head coach with immediate effect and that the process to appoint a successor is under way," a statement said.
"He leaves with a Premier League title to his name and our deepest gratitude and appreciation."
Liverpool stumbled to fifth place to secure Champions League football after taking just two points from their last four matches.
The timing of the decision, while welcomed by a large proportion of the fanbase, will anger those supporters who were clamouring for former midfielder Xabi Alonso to return to Anfield only for him to join Chelsea less than a fortnight ago.
Iraola was already one of the bookmakers' favourites even before Slot was sacked, while Germany boss Julian Nagelsmann and Paris Saint-Germain manager Luis Enrique are also high up on that list.
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In a statement owners Fenway Sports Group said: "That this was a difficult decision for us to make as a club goes without saying.
"We would like to take this opportunity to place on record our appreciation for Arne, who will always hold a special place in the history of this football club as the coach who delivered Liverpool's 20th league title.
"That accomplishment -- made all the more remarkable as it arrived in his very first season in charge -- was built on outstanding coaching and leadership every single day.
"He also helped guide the club through one of the most difficult periods imaginable following the loss of Diogo [Jota, who died in a car crash last summer].
"Nevertheless, the conclusion we have come to is built on a belief that the team's trajectory is best addressed through a change of direction."
Information from ESPN's Beth Lindop, as well as PA, contributed to this report.