Lingard is attracting interest from West Ham, who currently lead the race for the 28-year-old, while Williams has been linked with a temporary move to Southampton and Newcastle United.
United are also open to letting Facundo Pellistri leave on loan, with Solskjaer confirming on Tuesday that several clubs are interested in the 19-year-old winger.
The United manager stressed, however, that any loans would have to be right for both United and the player in question.
“[Lingard and Williams are] still part of the club, part of the squad. No deal has been struck for any players yet going out,” Solskjaer said.
“There have been many few 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 are Man United people and players through and through.”
Pellistri is yet to make his first senior appearance for United having joined from Penarol in a €10m deal on the final day of the summer transfer window.
“There have been talks and quite a few clubs are interested in Facundo to go out on loan,” Solskjaer confirmed. “That’s something we may do. We want him to have regular football at a high level.”
Lingard’s move to West Ham may hinge on the east London club’s ability to sign either Said Benrahma or Craig Dawson, who are currently on loan from Brentford and Watford respectively.
Premier League rules only allow two domestic loan players per club at any one time.
Sergio Romero and Marcos Rojo have also been given permission to speak to other clubs ahead of their contracts expiring at the end of the season.