The 22 year-old will kickoff tests on Monday with the Eredivisie outfit.
Borthwick-Jackson still has a year to run on his contract, but Heerenveen are banking on United releasing him should he do enough to win an offer.
He spent last season on-loan with Scunthorpe United.
Borthwick-Jackson made his debut for United in the 2014/15 season under then manager Louis van Gaal. He has subsequently been loaned to Wolverhampton Wanderers, Leeds United and also Scunthorpe United.