The 22-year-old joined Pools from neighbours Middlesbrough in the summer and has gone on to make 23 appearances for the Sky Bet League Two side.
Burgess, who has played just once for Middlesbrough, is hopeful he will be given the opportunity to play regular first-team football beyond the end of December, when his loan deal runs out.
"I would like to see out the season, but it is out of my hands at the moment," Burgess told the Hartlepool Mail.
"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."