Solskjaer keen to convince De Gea, Martial to stay at Man Utd
United have activated one-year extensions for both players in recent weeks, meaning they are tied to the club until the end of next season.Â
But forward Martial and goalkeeper De Gea remain locked in talks with executive vice-chairman Ed Woodward over longer deals with no sign of an end to the impasse imminent.
Solskjaer, who himself is only under contract with the Premier League club until the summer, may have limited say in United's long-term strategy.
But the popular former United forward, who has made an early case for the job on a permanent basis with comprehensive victories over Cardiff and Huddersfield in his first two games in charge, clearly hopes to leave his mark at Old Trafford by helping secure the services of two key players.
"I know the club want them to sign, of course, because they are top quality players," said Solskjaer.
"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.Â
"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."
Solskjaer, whose appointment as interim manager in place of the sacked Jose Mourinho has proved hugely popular with the club's fans, spent 11 years as a player with United until injury ended his career in 2007.
And he revealed that he rejected numerous opportunities to leave the club, and land a more cast iron guarantee of first team football, during his spell under Alex Ferguson.
"I had loads of offers and possibilities to move but the manager (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," said Solskjaer.
"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.
"If you are a regular at Manchester United, I think you should grasp the opportunity to stay here and become part of the history."
Martial's agent Philippe Lamboley was a vocal critic of Mourinho, while De Gea saw a move to Real Madrid fall through in 2015 and has been linked with Paris Saint-Germain and Juventus in recent times.
But Solskjaer, who is hoping to have all of Martial, Alexis Sanchez and Romelu Lukaku back available for Bournemouth's visit on Sunday, believes Martial could feature more as a central striker than he did under Mourinho.
"He can play as a number nine, of course, because he's got strength and he's good at holding the ball up," said Solskjaer. "But he is fantastic at one-on-one, so he can also play on the left or right wing.
"I've had chats with him and he can play in all those positions.
"As a defender you don't want to be dropping off towards your own goals with him running at you. So we need to get Anthony facing forwards."