Tottenham have been linked with the 27-year-old, offering him a lifeline to revive his career and force his way back into Gareth Southgate's England plans.
Jose Mourinho is keen to link up with the midfielder at White Hart Lane, according to recent reports.
Solskjaer was asked about Lingard's future after the full-time whistle at Kenilworth Road but he kept his cards close to his chest.
"I thought he was bright and was getting closer to a goal," Solskjaer deflected. "Bright and busy I thought."