Keogh started his career at Leeds and returned to Elland Road in August after struggling to establish himself at Wolves.
He has not made a Premier League appearance for Wolves since August 2010 and, after spending most of last term on loan at Cardiff City and Bristol City, has scored twice in 21 games for Leeds this campaign.
The Republic of Ireland's loan expires on 2nd January and the 25-year-old is eager for the two clubs to agree a deal so he can remain with Simon Grayson's side.
"I love the club and in an ideal world, I'd like to stay," Keogh told the Yorkshire Post. "It's up to the club and my agent will start speaking to them soon and to Wolves to see what the story is and we'll just go from there. I'll listen to what they have got to say.
"Leeds is a great club. It's the first club I signed for as a youngster and holds a place in my heart and I'm really enjoying my time here and it's a great dressing room.
"We've also got a really good chance of going up."
Reports have claimed that Wolves could offer Keogh as part of a cash-plus-player deal for Leeds striker Ross McCormack, who has been linked with a January move to Molineux.