The midfielder’s current deal expires at the end of the season and he has admitted his unhappiness at being a fringe player at Old Trafford, having enjoyed a storming loan spell at West Ham last year.
But a new contract is on the club’s agenda and manager Solskjaer has accepted that he will have to give Lingard more opportunities to convince him that his future is in Manchester.
"Jesse's had a good start to the season,” the Norwegian said on Friday. “He's come on and scored a few goals, that's been very important for us.
"We want to prolong his contract, we see him as an important player. It's up to him, maybe up to me, to give him more playing time because he deserves to.
"Hopefully, we can get a deal sorted for Jesse because we really rate him."
Lingard, 28, has scored two goals in six games this season but only one appearance has come as a starter. Saturday’s trip to Leicester could see him dropped even further down the pecking order with Marcus Rashford due to return.
One opening in the line-up could come if Cristiano Ronaldo is rested during United’s busy fixture schedule ahead, a tactic that Solskjaer has told fans to expect.
“It's hard to leave him out and I think everyone would love [it, for example] if you played six games in six days and played the same XI every time,” he added. “But we need to get to April/May with everyone firing.
"We got to May in the final stretch of last season and we were too tired. I manage the players for the club. It's nice to have him on the pitch, he'll always come up with the goods. The more we have him on the pitch, the better."