The 22-year-old, who is a former Arsenal youngster, has impressed for the League Two side since joining on a temporary basis in the summer.
He told the Sunderland Echo: "I would like to see out the season, but it is out of my hands at the moment. I would love to stay and it has been fantastic so far.
"I haven't spoken to Boro and I suppose we will see how it goes and then we will have to see what they say and what the gaffer here says and then decide what is best for both parties."
Burgess has made 15 appearances this season.