The Spanish international has emerged as Paris Saint-Germain’s number one choice after contract talks with United stalled over his £350,000 a week wage demands.
It is known that United have had a long standing interest in Everton star Jordan Pickford, who initially caught the eye of Jose Mourinho last year helping England reach a World Cup semi final.
Pickford’s form for Everton has dipped this season but he is still very much on Solskjaer’s radar even though Manchester United may have to pay as much as £60million to tempt Everton into selling.
While Atletico Madrid’s Slovianian international Jan Oblak is also on their wanted list but the Red Devils may have to pay a world record fee for a keeper to land him.
Chelsea splashed out £71m to Athletic Bilbao for Kepa Arrizabalaga last summer and Atletico rate Oblak at around £85m.
De Gea wants to become United’s best-paid player alongside Alexis Sanchez if he is to sign a new deal.
Sanchez is believed to be on £500,000 per week, though is not a regular first-team player whereas De Gea is key to United’s success.
The Spaniard has won four of the last five Player of the Year awards at United and wants that importance reflected in a new contract.
Real Madrid were also keen on De Gea, though signed Thibaut Courtois from Chelsea last summer.
And goalkeeping coach David Preece believes United should pay De Gea what he wants.
“In the past, your goalscorers earned the top dollars,” Preece, now coaching at Ostersunds, said.
“But with the importance of goalkeepers now, he has to be up there. Sometimes in the past managers looked at their budgets and whatever’s left over is what they have for a goalkeeper. Those days are over now.
“You look at David de Gea now and Alexis Sanchez is out the side and not really repaying the club in terms of goals and form, David de Gea has been so important for Manchester United over the last four, five, six seasons.
“Things haven’t been great since Sir Alex [Ferguson] left, but they’d be a hell of a lot worse if it wasn’t for David de Gea as well.
“He’s won a lot of points for them and he should be rewarded. He’s so important to that club now – it would give United a massive headache replacing him.”
Manchester United host Barcelona in the first leg of their Champions League quarter-final on Wednesday.