The Swede shot a superb 63 to hold off the challenge of Phil Mickelson and win the Claret Jug after a memorable duel a year ago.
Stenson climbed up the leaderboard to three under with an impressive five-under-par 65 in Saturday's third round but, with scoring conditions favourable, he expects to have to raise game yet further.
He has now been priced up by Sky Bet at 50/1 by Sky Bet to follow up those heroics in Scotland with a round to go.
The 41-year-old said: "It might well have to be something like that (at Troon), depending on what the last couple of groups are doing. If they keep on making birdies, that 63 might not even be good enough.
"But we'll see. I'm just happy with the way I played today, and should move up in the result list and hopefully get closer to the leaders."
Stenson carded six birdies in his third round and dropped just one shot, on the sixth. On a day when South Africa's Branden Grace recorded the first round of 62 in a men's major, Stenson felt he could have gained some more strokes.
He said: "I think we could have been sniffing around those numbers as well. I made some great putts out there but I also had a couple that were really close and I didn't take advantage of 17 the way I would have liked to.
"I don't think it would have been impossible for me to shoot a similar number today but I'm happy with the 65."
Stenson's latest Open challenge has been disrupted by a burglary at his rented house on Thursday. Stenson has tried not to let the incident unnerve him but it caused him unwanted stress.
He said: "It's obviously not a nice incident or anything you want to go through, but it was more the hassle - I didn't want to tee it up like I looked in Doral a couple of years ago. Standing in my boxer shorts on the first fee would have been so-so.
"It was all the mess getting everything organised, getting my clothes fixed and be back ready to play golf.
"It's some sort of disturbance and I spent those fours hours, instead of relaxing, watching a movie and chilling out, having to do other things."
