United have a number of players coming towards the end of their contracts, with Ander Herrera and Juan Mata set to expire in the summer.
David de Gea and Anthony Martial are reportedly in negotiations over new deals, which expire at the end of next season.
Both players would have seen their terms one to an end this season but they had a contract clause triggered which extended each contract by a year.
And Solskjaer has given an update on the situation, telling United fans that good news should be on the way regarding Mata, De Gea and Martial.
“I think the club’s making progress,” he said.
“But I leave that to the right people to do that.
“I don’t know really how far we are away from it, but hopefully we’re going to have some good news in the coming weeks.”
Meanwhile, the Norwegian has spoken out on Arsenal’s attempt to sign Eric Bailly this month.
Unai Emery is desperate for defensive cover after the loss of Rob Holding for the rest of the season.
However, without any transfer funds only loans can be made this month.
Bailly had emerged as a potential target because of his game-time situation, where he is being kept out of the starting XI by the likes of Victor Lindelof, Chris Smalling and Phil Jones.
But the Old Trafford outfit rejected any move for the Ivorian, and Solskjaer has not spoken out on the transfer.
When asked about the interest, Solskjaer said: “I’m not surprised if they do. That’s just one of those things.
“There’s always speculation and it’s not a big surprise.”
It adds another layer of subplot to the highly-anticipated FA Cup clash between the two Premier League titans tomorrow night.
United travel to London to take on the Gunners at the Emirates, in what should be the game of the round.