The 31-year-old ended his reign as the club's longest-serving player following the expiration of his contract earlier this summer.
The centre-back had played just 13 games in the past four seasons for the Red Devils, who he signed for in 2011 from Blackburn.
It was reported on Tuesday that the 27-cap England international was set to return to United on a coaching role.
But according to the Manchester Evening News, those claims are wide of the mark, with the defender just observing academy games.
Since leaving Old Trafford, Jones is yet to find a new club, and MEN state that he has been watching training sessions involving United's youth teams at Carrington over the past weeks.
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The news outlet then insisted there are no plans for Jones, who is still deciding on his next career move, to join the academy coaching staff on a permanent basis.
It's not uncommon for ex-players to spend time at the academy after leaving, imparting their wisdom on the next group of potential first team stars.
Jones was entitled to a testimonial match by virtue of spending a decade with United, but he turned the opportunity, reportedly joking, 'apart from my mum and dad, who else would turn up?'
A Premier League winner under Sir Alex Ferguson in 2013, Jones featured 229 times for United in all competitions.
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But with so few appearances over the past five years, his departure was inevitable, though he still showed plenty of emotion when saying goodbye to the club in May.
"My time at United has been nothing short of incredible," Jones said in a statement.
"To wear this shirt just once, to wear this badge and represent everyone associated with it, was an honour.
"I wish I could have played more. I wish I could have given more to the many squads I played alongside.
"I will say from the bottom of my heart, I did everything I could. I did everything the medical team asked of me."