Kieran McKenna has been urged to stay at Ipswich Town unless a 'big club' comes in.
However, that will not be Bournemouth, according to Tractor Boys legend Alan Brazil.
Kieran McKenna the head coach / manager of Ipswich Town at full time during the Sky Bet Championship match between Middlesbrough and Ipswich Town
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McKenna has been told to snub Bournemouth this summer if Ipswich are promotedCredit: Getty
McKenna has emerged as a candidate to succeed Andoni Iraola at the Vitality Stadium this summer.
It was confirmed on Tuesday that the Cherries boss will leave the club at the end of the season.
Iraola is set to depart after three years in charge, with Bournemouth now searching for a replacement.
talkSPORT understands ex-Borussia Dortmund manager Marco Rose is the frontrunner with McKenna also being considered.
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Coventry City's Frank Lampard has also been rumoured to be a target but is not on Bournemouth's shortlist.
Should McKenna leave Ipswich?
Brazil discussed the situation on Wednesday's Breakfast show alongside Katie Shanahan and Ally McCoist.
Reacting to Lampard and McKenna being linked with the job, he said: "That’s bad, though, isn’t it? Frank’s done a great job. He’s going to win it (the Championship) with Coventry. Hopefully, Ipswich will be second or go through the play-offs.
"I’d rather not speculate, but two that have still got a lot to do. There’s so much at stake at the moment.
"Particularly if, and Frank’s a certainty, those two clubs get promoted, would they go to another club? Maybe not."
Ipswich are currently second in the Championship as they chase an immediate Premier League return.
Andoni Iraola reacts during the English Premier League football match between Arsenal and Bournemouth
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Iraola will leave his role as Bournemouth boss at the end of the seasonCredit: AFP
McKenna's side are two points clear of third place Millwall with a game in hand despite losing to Portsmouth on Tuesday.
However, the Tractor Boys must still face promotion rivals Middlesbrough and Southampton in their final five matches.
Are Bournemouth a 'bigger club' than Ipswich?
Later in the show, Brazil was asked if he can see McKenna staying at Portman Road if Ipswich are promoted this season.
He replied: "Unless a big club come in, because we’ve got American backers and there is money there."
McCoist then quipped that Brazil had suggested Bournemouth are not a 'big club'.
The former forward hit back, exclaiming: "They’re not bigger than Ipswich.
Alan Brazil reacts on talkSPORT Breakfast
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Brazil dismissed the suggestion that Bournemouth are 'bigger' than IpswichCredit: talkSPORT
"Bournemouth? What have Bournemouth won? You’re having a laugh aren’t you?
"Look, honestly Ipswich are a bigger club than Bournemouth. I think Bournemouth have been brilliant, friendly club but no, no, no."
Bournemouth are yet to win a major trophy in their 127-year history.
However, the Cherries did equal their highest-ever league finish of ninth last season.
Iraola could also secure a maiden European campaign before he leaves, with his side two points adrift of the top seven with six matches still to play.
As for Ipswich, the Tractor Boys have won the FA Cup and UEFA Cup as well as a league title back in 1962.
Dango Ouattara of AFC Bournemouth celebrates with teammate after scoring his team's second goal during the Premier League match between Ipswich Town FC and AFC Bournemouth
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Bournemouth won at Ipswich last season, but were beaten at home by McKenna's sideCredit: Getty
Brazil was part of the side which beat AZ Alkmaar in the 1981 UEFA Cup final.
Who will be next Bournemouth manager?
McKenna is a potential option to replace Iraola as Bournemouth boss, talkSPORT understands.
The Northern Irishman is seen as expensive appointment by the Cherries, though.
Having signed a new deal at Portman Road two years ago, his current contract runs until the summer of 2028.
McKenna guided Ipswich from League One to the Premier League following his appointment four-and-a-half years ago.
Rose is currently the leading candidate to succeed Iraola in the dugout on the south coast.
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Jaden Philogene-Bidace of Ipswich Town celebrates scoring their first goal during the Sky Bet Championship match between Norwich City and Ipswich Town
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Ipswich are second in the Championship as they chase a Premier League returnCredit: Getty
Talks have already been held with the German coach regarding a potential appointment.
Rose is available after leaving RB Leipzig in March 2025 and has previously managed RB Salzburg, Borussia Monchengladbach and Borussia Dortmund.