The ex-England international was sacked as Cherries boss at the end of August after just four Premier League games in charge.
Gary O’Neil has been in temporary charge of Bournemouth since Parker’s dismissal, and has overseen three games, winning once and drawing the other two.
The Cherries are yet to appoint a new manager since their improved form under O’Neil, but will likely want to have a permanent boss in charge for their next league game against Brentford on October 1.
With Bournemouth yet to confirm a new man at the helm, it’s no surprise a number of candidates have been linked with the job.
Who is favourite for the job?
As per SkyBet, Sean Dyche is the favourite to be the next Cherries’ manager, and is priced at 11/8.
Current interim-boss O’Neil can be backed at 2/1, while Kjetil Knutsen is 6/1.
Next is Sam Allardyce (8/1) and then Nathan Jones at a price of 10/1.
Other names being mentioned include Marcelo Bielsa, Chris Wilder, Harry Redknapp, John Terry and Jonathan Woodgate.
The experienced manager has been out of work since the end of the 2020-21 campaign, when he left Albion after failing to keep them in the Premier League.
Despite the relegation, he has a track record of keeping troubled clubs in the top flight, though fans of his previously managed teams have expressed their displeasure of his style of play.
The 67-year-old hasn’t ruled out returning to management if the right opportunity were to arise.
Speaking on the Kammy & Ben’s Proper Football Podcast, Allardyce said: “Never say never. I’m never going to say never now, whatever might happen. If it feels right and I fancy it, then I’ll have a go.”