Ed Sheeran has agreed a one-year deal to take over as principal sponsor for both the men's and women's team at Ipswich.
Referee Darren Drysdale has been charged with improper conduct by the FA after confronting an Ipswich Town player.
Former Tottenham, Arsenal and England defender Campbell is eager to get into management and was linked with the job at League One side Oxford.
McCarthy, who has come under increasing pressure from fans this season, had originally said that he would go at the end of the campaign.
Birmingham lifted themselves out of the bottom three with a 1-0 Sky Bet Championship home success over Ipswich.
Mick McCarthy will not renew his contract with Ipswich Town at the end of the season, the club has confirmed.
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