The Red Devils are in disarray after a 5-0 mauling at the hands of fierce rivals Liverpool at Old Trafford on Sunday compounded a poor start to the season with Solskjaer fearing his time in charge may be coming to an end.
The club have drawn up a four-man shortlist of potential successors including the out-of-work pair, as well as Leicester's Rodgers and Ajax's Ten Hag.
United chiefs are said to have told a prominent agent to get in contact with several leading managerial names to discern their contract demands and vision for United if they took over.
Although the Red Devils remain reluctant to sack Solskjaer, having handed him a three-year contract extension in July, the Liverpool capitulation could force the club's hand.
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