But the Welshman is facing a dilemma as he has increased competition at the Bernabeu this season.
Marco Asensio and Isco have both emerged as serious threats to his position under Zinedine Zidane.
Spanish outlet Diario Gol claim Bale does not want to leave as he sees Real as the best team on the planet right now.
But they also report the 28-year-old’s relationship with Isco is strained.
The two reportedly do not speak more than strictly necessary following Real’s pre-season tour of the United States.
Manchester United (Odds: 1/3 to win, 9/1 to lose, 4/1 to draw)
Red Devils supremo Ed Woodward tried to sign the forward but he opted to make a switch to Real instead.
The Wales international missed much of last season due to injury problems.
Bale made just 19 La Liga appearances and started on the bench in Cardiff for the Champions League final in which Real won.
United have made three summer signings so far, bringing Victor Lindelof, Romelu Lukaku and Nemanja Matic to the club.
Jose Mourinho’s side return to action tomorrow lunchtime when they travel to Swansea in the Premier League.