The Dutchman's future is under huge scrutiny at Old Trafford, with new minority owner Sir Jim Ratcliffe heavily rumoured to be looking to replace him in the summer.
One name that Ratcliffe is said to be keen on is England boss Southgate, and despite some fans sceptical of the choice, O'Hara told Grosvenor Sport he'd be in favour of the appointment.
“I think that if Gareth Southgate were to go to Manchester United after the European Championship, it would be a good appointment,” he said.
“There is speculation that he may not be able to deal with the pressure that comes with the Manchester United job, but I’d say that the England job comes with just as much scrutiny and he’s dealt with it and conducted himself very well.
“People forget that he’s changed things at England – he’s changed the mentality of wanting to play for the national team. The players seem to love their time in the England squad and Southgate is the reason for that – he’s made the team feel like a close-knit club.
"That is exactly what Manchester United need – their team feels like a group of individuals at the moment.”
The former Tottenham midfielder also pinpointed Southgate's ability to work with young players as a huge selling point, especially given the young talent Man United have at their disposal.
Adding: “Southgate has also showed his ability to work effectively with young players, bringing out their best qualities and aiding their development on the international stage.
“You look at all the young talent United have at their disposal –Alejandro Garnacho, Antony, Kobbie Mainoo – I think they could benefit from Southgate's guidance and support.”
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