The 29-year-old joined Neil Warnock's team on loan from the Premier League side and wants to extend his stay at Elland Road when the transfer window reopens in January
The 29-year-old joined the Potters in 2008 after playing for Neil Warnock at Sheffield United, but has been unable to gain a role in the starting XI for Tony Pulis' side.
And although the midfielder is appreciative of what the Premier League side has done for him in the past, he feels it is time to find a permanent role in a team where he will play regular games.
"I'd love to stay on beyond this loan spell," he told reporters. "My ideal scenario would be to stay at Leeds for the rest of the season."
Tonge has only played 19 times for Stoke, and feels now is the time to try and cement a future for himself in football - and would like to continue his relationship with Warnock at Elland Road.
He added: "Tony Pulis has been great with me and always helps me to find new places to play on loan but sooner or later I'd like to settle down.
"Not knowing how long you'll be with a club isn't easy and I don't really like being in no-man's land."
Leeds play Middlesbrough on Saturday in what will be the last game of Tonge's current deal, with his other spells coming at Preston (twice), Derby and Barnsley.