The Wales international moved to the Spanish capital from Tottenham Hotspur in 2013 for £85m but after initial success has fallen down the pecking order due to a succession of injuries and lack of form.
Kylian Mbappe's much-rumoured arrival at Real is expected to lead to the departure of a big-name player in Zinedine Zidane's squad and reports have suggested the La Liga champions could fund the acquisition of the France international with the sale of Bale to United.
The 18-year-old Ligue 1 star is a summer target for Real and United's Premier League rivals Manchester City. Pep Guardiola's side have been linked with making a £143m ($186.2m) bid for the attacker, who scored 26 goals and registered eight assists across all competitions last season.
Real will face competition from the Etihad Stadium outfit in pursuit of Mbappe and City believe that they could offload Bale to United top ensure they have the necessary funds in signing the teenager.
Bale has already expressed his desire to remain with Real, to whom he is contracted until 2022. A source close to the player has now claimed that "nothing has changed" regarding the winger's future at the Bernabéu and will be at the club beyond the end of the summer transfer window.
IBTimes UK also understand that Jose Mourinho's team are aware that Bale is not keen on leaving Real and have never made any effort to sign him.
How Bale's retention at Real affects any deal for Mbappe remains to be seen but it could yet give City, whose manager Guardiola has been coy on his interest in the player, new hope in beating Zidane's side to his signature.