The Spanish side have identified De Gea - who will soon enter the final year of his current contract with United and has so far declined to sign an extension - as the ideal replacement for Iker Casillas and have issued the 24-year-old an ultimatum to persuade him to join this year.
Cech, meanwhile, is ready to leave Stamford Bridge after being displaced as Chelsea No.1 by Thibaut Courtois this season and his agent, Viktor Kolar, on Tuesday revealed that his client would be open to joining United or Arsenal.
Scholes sees Cech as the outstanding available candidate to replace De Gea should he depart and believes the 33-year-old could have a similar impact at Old Trafford as Dutch goalkeeping great Edwin van der Sar.
"If De Gea does go, United should sign Petr Cech," Scholes wrote in his column for the Independent.
"I remember the effect Edwin van der Sar had on the club when he arrived in 2005. United had struggled since Peter Schmeichel to find a really commanding goalkeeper. Fabien Barthez was the closest we got.
"Edwin came ready-made. He was a Champions League winner, he had four years’ Premier League experience with Fulham, and in the end our manager got six extremely successful years out of him.
"Edwin was almost 35 when he joined United. Cech has only just turned 33. He could potentially play another six years for United.
"There would be no concern about having to give him time to play his way into the position or the demands that the Premier League makes of a goalkeeper new to the country. United won’t want to lose De Gea but there is a solution in the offing."
