The World Cup winner has fallen out of favour at Old Trafford and has not started in the Premier League since a 1-0 defeat to Crystal Palace in September.
He's fallen down the pecking order and talkSPORT understands Varane was very unhappy at being dropped for the Manchester derby at Old Trafford last month, which United lost 3-0.
According to The Sun, Varane is planning a departure but Ten Hag will not sanction any exit in January with the squad already depleted.
It means a summer transfer is now the most likely avenue for the former Real Madrid star, who already has plans on his next destination.
talkSPORT also understands that prospective co-owner Sir Jim Ratcliffe will look to move on Varane and midfielder Casemiro.
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Contrary to reports in Spain, a return to Real Madrid for Varane is highly unlikely.
Instead, a Saudi swap looks more on the cards where former United stars Cristiano Ronaldo and Alex Telles have already made the move.
But if he wants to stay in Europe, signing for a club in Italy is his most likely destination.
Juventus are keen on a centre-back, as are Inter Milan after losing Milan Skriniar to Paris Saint-Germain in the summer on a free transfer.
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However, matching his £340,000-a-week wages at United might prove a stumbling block for any potential suitor.
Varane has recently fallen behind Jonny Evans in the pecking order at United, who was a shock signing after being released by Leicester in the summer.
However, Ten Hag likes having a left-footed defender at the back while his usual deputy, Lisandro Martinez, is out injured.
Harry Maguire has returned to form and forced Varane out of the side while Victor Lindelof has had to be used as an auxiliary right-back with Aaron Wan-Bissaka sidelined and Diogo Dalot covering for the crocked Luke Shaw.
A source told The Sun: "There's already interest from Saudi Arabia where Varane could pocket a massive uplift in his wages.
"But he's also keen on Italy as it's a league he admires and would love to be a part of."
Varane joined United in 2021 and the signing was hailed as a marquee arrival after huge success with Real Madrid, including three Champions League titles in a row.
Last season, the Red Devils had one of the best defensive records in the Premier League with Varane partnered with Martinez.
They finished the season with 17 clean sheets, the most in the division and three more than Liverpool, Newcastle and Arsenal.
However, this campaign has seen a turnaround with United struggling in defence while Ten Hag insisted there was no fallout between him and Varane.
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The Dutchman claimed: "It is about tactical reasons why I chose these partnerships. I think Harry and Jonny did well.
"What I said last year, Harry didn't play a lot, so I was very happy with Rapha's performances. I have always been happy with his performance."