For several seasons, the La Liga giants have been keen on giving De Gea a route back to Madrid, where the stopper has previously represented Atletico.
However, a combination of paperwork issues, a fresh contract for De Gea and the reluctance of United to sell one of their key men has led to a transfer never materialising, but it appears that Zinedine Zidane is planning another approach.
According to The Mirror, Real are willing to make an offer of £46m in an attempt to push through the signing of the 26-year-old.
At this stage of the window, United are only likely to entertain bids in excess of their valuation, but De Gea has just two years remaining on his deal at Old Trafford.
In six years in the North-West of England, De Gea has made 271 appearances in all competitions.