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.
Mitchel grew up in London while his old man, now 51, was making history for Arsenal and featured for local side Hadley Wood Rangers.
