Lingard, who is a target for West Ham, and Williams have been on the fringes of the first-team squad this season and struggled for game time.
Solskjaer says any move must suit the club and the players.
"They're still part of the club, part of the squad, and no deal has been struck for any players yet going out," said the United boss.
"There have been many clubs interested in our players, so let's see what happens. It's important to take our wishes and our plans into consideration, but the players as well of course because they are Man United people and players through and through."
Solskjaer is prepared to let 19-year-old right winger Facundo Pellistri go out on loan to Spain for first-team experience. However, 18-year-old winger Amad Diallo will stay at United and push for a senior debut having only arrived from Atalanta earlier this month following the completion of his £37m move.
"There have been talks and quite a few clubs interested in Facundo to go out on loan and maybe that's something we'll let him do. We want him to have football at a high level," said Solskjaer.
"With Amad, it's a different scenario. He's had a good training regime and programme, he's doing well and it won't be too long until I can bring him into the squad."