The 28-year-old spent the second half of last season on loan at West Ham United, where he scored nine goals and provided five assists in 16 Premier League games.
Lingard has since returned to United for pre-season training but he is currently self-isolating, after testing positive for coronavirus.
The 24-year-old has been heavily linked with a transfer to the Emirates Stadium, though the Gunners would need to fork out in excess of £60m if they were to recruit the playmaker this summer.
Lingard, who has entered the final year of his contract at Old Trafford, would be willing to leave United if he knew he would get regular first-team football elsewhere. body check tags ::