The 20-year-old Middlesbrough winger has excelled since joining the Hornets, scoring three times in six appearances for Boothroyd's side - including the opening goal in their 3-1 over Scunthorpe at Glanford Park last weekend.
"I'd like to keep Adam for the season, but I'll have to have a chat with Gareth Southgate first," Boothroyd told the Watford Observer.
"It's important in situations like these that the communication lines are kept open. I've given Gareth the same treatment I did with Sir Alex Ferguson when we had Ben Foster.
"He knows what I think about the player. Adam is thriving at being given the opportunity to play regularly and he's learning his trade."