The legendary Blaugrana midfielder is said to have emerged as a leading contender to take charge of the Red Devils over the past few days, and chief executive Omar Berrada apparently flew out to Spain to hold talks with him earlier this month.
Ten Hag's future remains the subject of unrelenting speculation, although he managed to buy himself a bit more time with a nervy 2-1 Premier League win over Brentford last weekend.
However, should the Dutchman fail to lead his side to positive results against Fenerbahce in Thursday's Europa League clash and against West Ham United in the Premier League this weekend, INEOS could act.
Ten Hag has already overseen Man United's worst-ever start to a top-flight campaign, as the 20-time English champions languish in 12th place in the table, taking just 11 points from their opening eight fixtures.
Xavi 'wants to bring Raphinha to Man United'
According to Fichajes, Xavi would be willing to take the reins at Old Trafford, but only if the powers-that-be can strike a deal to sign in-form Barcelona attacker Raphinha.
The former Leeds United man - who snubbed interest from a few Premier League teams to join the Blaugrana in 2022 - has hit a rich vein of form this season with a whopping nine goals and eight assists in 13 matches in all competitions.
Flourishing under the wing of Hansi Flick, the 27-year-old scored a hat-trick in Wednesday's 4-1 Champions League thrashing of Bayern Munich, where he also wore the captain's armband.
Raphinha is still contracted to Barcelona for another three years, but the report claims that the La Liga leaders would still be open to selling if an interested party stumped up a bid of €100m (£83.3m).
Such a transaction would make Raphinha Man United's second-most expensive signing of all time, above Antony and only behind Paul Pogba, but the player's will must also be taken into account.
Could Raphinha replace Marcus Rashford at Man United?
The 27-year-old was heavily linked with a move to Saudi Arabia in the summer before making it clear that he wanted to prove himself at Barcelona, where he has come up with 29 goals and 33 assists in 100 appearances.
Raphinha's prospective arrival in Manchester could push Marcus Rashford out of the door, as the report adds that the Red Devils are still considering offloading the Englishman amid his renewed struggles this season.
Rashford only has one goal and one assist to show from eight Premier League appearances, and the club are also looking for a new stomping ground for the under-performing Antony, who is allegedly wanted by a number of top-flight teams on loan in January.
Xavi supposedly believes that the signing of Raphinha would give Man United a new dimension in attack, and the Brazilian could be the key to helping the Red Devils establish themselves as a force both in England and on the continent again.
Whether a deal can be agreed for the Spaniard to take charge of Man United is another matter entirely, though, as uncertainty continues to linger over Ten Hag's long-term future.