In an interview with talkSPORT, Arsenal legend Ray Parlour has suggested that United should attempt to sweeten the deal to land the Wales international with the services of Sanchez.
Having joined Real in 2013, Bale has seen a lot of success with Los Blancos, winning a La Liga title and four UEFA Champions League trophies during his time in Spain.
However, the Wales international has always cut a somewhat unsettled figure at the Santiago Bernabeu.
Given that Zidane had reportedly advised Florentino Perez to sell Bale last summer only, an exit from the Bernabeu in the upcoming window seems a strong possibility for the Welshman.
And former Arsenal midfielder Ray Parlour has advised Manchester United to capitalise on the situation and swoop in for the 29-year-old.
Parlour further goes on to claim that throwing in the Chile international as part of the deal would strengthen the chances of The Red Devils landing the former Spurs forward.
"Sanchez was in such great form at Arsenal. I know a lot of Manchester United fans and I said to them, ‘You got an absolute bargain there – £20million for a player of his calibre – he’s going to make your team much better'."
"He was brilliant at Arsenal. I do like him. He was one of those players who you would pay to watch. It just hasn’t happened for him. I’d go to Real Madrid and I’d swap him for Gareth Bale. They’ll be on the same sort of wages."
Bale, with his immense experience in England and on the continental stage, could be a prize catch for the 20-time English champions.
Sanchez, on the other hand, has had a torrid time since switching Arsenal for United in January last year and could be shipped out given his status as the highest paid player in England with his £500,000 (R9.5m)-a-week wages.