But Rovers manager Dean Saunders said a deal had not been completed and expected Boro to face competition for the player, who was linked with a move to Charlton last week.
"If George goes I'll be really disappointed," Saunders told the press after Saturday's 3-3 friendly draw at Bradford Park Avenue.
"He's a good man, he has a great attitude and he's a great athlete. But we have to cut our cloth accordingly and we've agreed a fee with Middlesbrough, although I'm still expecting more interest from other clubs."
Friend, whose previous clubs include Exeter and Wolves, joined Doncaster on a free transfer two years ago.