United have been chasing Bale for a number of years, with former boss David Moyes revealing he came close to signing him at one point while Jose Mourinho has gone public with his interest in the Welshman.
Mourinho appeared to have given up hope after Bale figured in the Real side that beat United in the European Super Cup earlier this summer, but reports are suggesting a deal is back on ahead of the deadline.
Bale came in for heavy criticism after Real's 2-2 draw against Valencia at the weekend, forcing boss Zinedine Zidane to jump to his defense and insist that he is in his plans going forward.
It looked as though United would have to wait 12 months but they now sense the opportunity to strike a deal and reports have suggested they will try and tempt Los Blancos into selling by offering £97 million.
Real would have to move quickly to draft in a replacement although they may already have a ready-made one in the form of Marco Asensio, who is tipped to be a star of the future.