The England international is weighing up his options ahead of the summer market after falling off the first team radar for much of this year.
The Times says Newcastle United are interested, though a move abroad could be on for Lingard.
The 27 year-old is on the radar of Gladbach, while Roma are also monitoring developments.
Lingard intends to wait until United's Europa League campaign concludes before making a final decision. Contracted for another year, his deal also includes a 12 month option.