United have earmarked £100 million for Bale after losing out to Madrid in the race to sign the Welshman in the summer of 2013.
And the Spanish giants are ready to hand an ultimatum to the Red Devils by telling them that including De Gea will be the deal-maker.
Real have identified the 24-year-old as the goalkeeper to replace long-serving veteran Iker Casillas.
De Gea is in the process of taking over from Casillas as Spain’s No 1. and it is a matter of pride at the Bernabeu that the top Spanish keeper plays for Real.
United do not want to part with arguably the best in the Premier League in the three-and-a-half seasons since he arrived from Atletico Madrid for £18 million.
But there is growing concern at Old Trafford about the failure to secure De Gea on a new contract as he approaches the final 18 months of his current deal.
United believed they had a deal for Bale completed before the 25-year-old joined Real in a world-record £85 million transfer.
They have been made aware that the Spanish club will cash in on the former Southampton and Tottenham wideman at the end of the season after lining up Boussia Dortmund’s Marco Reus as a replacement.
But Madrid will still drive a hard bargain.
It cost United a British-record £60 million to land Angel di Maria last summer, even though Real were willing sellers and there was only one club in the market.
If United are unable to persuade De Gea to commit himself to a new long-term deal in the coming months, they will be faced with the prospect of losing him for nothing in the summer of 2016.