The Slovakia international made his Clarets debut in Sunday's 2-0 FA Cup third-round defeat against Premier League leaders Arsenal.
Varga, 35, agreed to a one-month loan at Turf Moor, but he has settled in quickly and is already looking further ahead.
"I always like to play and it was a great opportunity for me," he said.
"It was really nice for Owen Coyle to give me a call.
"I had other chances but I preferred this one and if Burnley would like to do it (extend the loan) then that would be good as I already like it here."