However, the Real Madrid star must wait until the summer for a transfer to be sanctioned by the La Liga champions.
Florentino Perez was hoping to use Bale as part of a swap deal with Tottenham for striker Harry Kane, according to Spanish outlet Diario Gol.
But the Welshman would rather link up with Jose Mourinho at Old Trafford once he has helped Real finish the season on a high.
The Portuguese boss tried to sign Bale last summer but was unable to secure a deal.
The winger’s immediate focus is on trying to rescue Real’s season by getting past Paris Saint-Germain in their Champions League tie.
Diario Gol add that an approach for Kane would cost around €300million (£262.9m) and a swap would soften the financial burden.
However, Perez could now use the 28-year-old as a bargaining chip to sign Man Utd’s David De Gea.
Real have been after the Spanish shot-stopper ever since Iker Casillas left the club in 2015.
They came close to signing him that summer but the move feel through because of a faulty fax machine.
Keylor Navas is Los Blancos’ current number one but he knows his position is under threat at the end of the season.
