De Gea is currently regarded as one of the top goalkeepers in world football and he is currently contracted to the Old Trafford outfit until the summer of 2020.
Martial is also under contract until 2020 but it is believed that the Red Devils are keen to get both players to commit to new long-term contracts.
Given the uncertainty about the future and direction of Manchester United, the two players may not be in any rush to put pen to paper on new deals.
The Red Devils sacked Jose Mourinho earlier this month and brought in Solskjaer as interim boss until the end of the season. It remains to be seen who will be in charge at Old Trafford at the start of next season.
However, Solskjaer has now confirmed that he wants to see both players commit their long-term futures to the Red Devils.
Speaking at a news conference before Manchester United’s clash with Bournemouth on Sunday, Solskjaer said: “I know the club want them to sign, of course, because they are top quality players.
“It’s down to the players, but when you’re at Man United there isn’t a lot of greener grass on the other side. You are at the best place. It’s the biggest club in the world.
“For me, I would hope I can help or guide these players to maybe tip them over to thinking they want to stay at this club.
“If you are a regular at Manchester United, I think you should grasp the opportunity to stay here and become part of the history.
“I had loads of offers and possibilities to move but the manager [Sir Alex Ferguson] sat me down and told me I was going to be an important part of his team, his squad, and I was going to play enough games.
“I felt privileged to play here. I am also stubborn. The club agreed to sell me to Spurs one time and I said, ‘No, thank you’. My agent wanted me to go but I knew I was at the best place.
“I wasn’t sure the grass was greener somewhere else. I had a period when I wasn’t playing. I would get angry. Then he [Ferguson] would put me in the team and I would feel a big part of it and important. But we’re not talking about squad players now – we are talking about top players.”
Manchester United are aiming to break back into the top four before the season is out as Solskjaer looks to try and lead the Red Devils to Champions League qualification for next season.
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