The publication claims the defender wants to try and win back his place in Mourinho's first-team, but will seek to leave if his prospects do not improve before the end of the season.
Bailly has been heavily linked with moves to Arsenal and Tottenham in recent weeks.
But ESPN claim United are unwilling to sell the centre-back unless he asks for a transfer.
Speaking after Bailly was subbed against Newcastle, former Manchester United star Rio Ferdinand claimed there was no way back for the defender.
Man Utd news: Eric Bailly is considering an Old Trafford exit (Image: Getty)
Man Utd news: Eric Bailly was hooked after 19 minutes (Image: Getty)
“This guy, I don’t see a way back for Bailly,” he said on BT Sport.
And fellow ex-professional Steve Nicol thinks all defenders at Old Trafford are on borrowed time - but rates Bailly as the best.
“Does any centre-back have a future at Manchester United?” Nicol told ESPN FC.
“If they get rid of them all they won’t have any.
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