The son of Arsenal legend Dennis Bergkamp is trialling at London Colney.
The Sun says the Gunners have watched 22-year-old Mitchel in action at their North London training ground this week.
Attacking midfielder Mitchel Bergkamp, a free agent, slotted in with the Under-23s and made a good impression on manager Steve Bould.
Mitchel has spent his entire career thus far with Dutch second-division side Almere after joining them in 2017.
He turned out for the youth teams but failed to make an appearance with the seniors.