Club sources have reiterated United are reviewing their season but do not expect an impending outcome.
United have notified representatives of potential replacements that they are considering retaining Ten Hag after he guided the club to their 13th FA Cup triumph over City on Saturday.
Ten Hag, 52, is under contract at United until next year and the club has the option of an additional year.
United have assessed a number of possible successors and have held dialogue with intermediaries in recent weeks.
Ipswich Town manager Kieran McKenna withdrew as a candidate to take over at Chelsea as his preferred destination would have been United.
Former United coach McKenna has been reluctant to rush into a decision after leading Ipswich Town back up to the Premier League and he is now expected to accept a substantial offer to sign a new contract with the club.
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