McKenna, 40, made the shock decision to stand down from his position as Ipswich manager to take a break from football earlier this month.
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The Northern Irishman had just earned promotion back to the Premier League for the second time, having been relegated in 2024-25.
According to BBC Sport, in their search for a new manager, Ipswich have added Solskjaer, 53, to their shortlist.
Solskjaer has been out of work since leaving Turkish side Besiktas in August 2025, just seven months after been appointed.
It’s been five-years since his spell as Man United manager, where he led the club to a second place finish in 2020-21.