That is the opinion of former United defender and now pundit Danny Higginbotham, who has suggested an exit is unlikely.
The Ivorian has been linked with a move to Arsenal this week as Unai Emery looks to bolster his defence.
The teams put their pursuit of the Premier League top four aside tomorrow night as they go head-to-head in the FA Cup Fourth Round.
Bailly fell out of favour towards the end of Jose Mourinho’s tenure but has now seen his game time increase since the arrival of Ole Gunnar Solskjaer.
And Higginbotham believes that there is hope for the defender after being asked whether he has a future at Old Trafford.
“I would think so [he has a future]. I still put him up there as one of, if not the best centre-back at the club at the moment,” he told Sky Sports News.
“I think at times [because of injuries] it’s been difficult to get a partnership going.
“His first game was Bournemouth away last season or the season before, he loves that scissor challenge and it was always going to come back to bite him and it did when he got sent off against Bournemouth [in December].
“But I do still believe that defensively, he can get dragged out of position at times, he’s one of, if not the best centre-back that United have.”
His manager Solskjaer was not surprised to hear that the Gunners might be interested in Bailly.
“I’m not surprised if they do [want him], to put it that way but that’s just one of those things there’s always speculation, it’s not a big surprise,” he said in his press conference.
The Norwegian was also quick to praise the impact his counterpart Emery has made since arriving in north London.
“Obviously Arsene Wenger and the gaffer are the two longest serving managers in my era, they were fantastic, an institution in the club,” he added.
“It’s going to take time but Unai, they beat us with Sevilla, and they’ve made a very good signing tactically he’s very good, high energy.
“I don’t know what team he’s going to play, he’s got loads of different tactics. They’ve made a very good signing.”
Arsenal and United are currently both locked on 44 points in the Premier League, three points behind Chelsea who currently occupy the final Champions League qualification spot.