Southgate has been one of a few names to be connected with the Old Trafford dugout with current boss Erik ten Hag facing pressure to keep his job.
Sir Jim Ratcliffe is set to make a decision on the Dutchman's future, and ex-Liverpool midfielder Jason McAteer says one current player hinted that Southgate has been lined up.
Talking to beIN Sports, McAteer said: "I had a conversation with him [the player] on Friday, I bumped into him because I live just outside the area... and I asked him about the end of the season and what his thoughts are.
"He gave me no inclination that the manager was there to stay. In fact, we spoke about different names and who he thought would be a good fit."
When pressed, McAteer added: "Yeah, that was the name [Southgate]. Footballers have an inclination when the manager's job is on the line and they obviously know and I just got the feeling that it's done, it's done."
M.E.N. Sport understands that Ratcliffe is not wholly sold on Ten Hag as United's long-term manager, having refused to assess his tenure publicly.
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