Marcos Rojo and Sergio Romero have been told their deals will not be extended beyond the summer, while home-grown full-back Williams has been linked with a temporary exit in search of first-team minutes.
Lingard, meanwhile, has only made three appearances this season and there has been interest from home and abroad, with a switch to West Ham reportedly in the offing.
Asked about the situation with Williams and Lingard, Solskjaer said: “They’re still part of the club, part of the squad, training well. No deal has been struck for any of the players yet going out – still a little period left, of course.
“There’s been many clubs interested in our players, so let’s see what happens.
“For me, it’s also important to take our wishes and our plans into consideration but also the players of course because they are Man United people and players through and through.”
Odion Ighalo will leave Old Trafford when his loan from Shanghai Shenhua expires on January 30, with the striker saying on Twitter: “It’s so hard to see this dream come to an end.”
Teenager Facundo Pellistri looks set to head out on loan. It is understood discussions have been held with a couple of clubs about the 19-year-old Uruguayan, who has yet to make his first-team debut since joining from Penarol in October.
“There has been talks and there’s been quite a few clubs interested in Facundo to go out on loan and that’s maybe something we will let him do now,” said Solskjaer, who completed a deal for Atalanta teenager Amad Diallo this month.
“He’s had a few games in the reserves. We want him to have regular football, of course, at a high level of course.
“With Amad, I think it’s a different scenario. He’s just come in, he’s going through a good training regime and training programme and he’s doing well. It won’t be too long, I feel, before I can bring him into the squad.”