The former Augusta State golfer holds down the 10th and final automatic qualifying spot in the standings. The Englishman is expected to make the team -- which will be determined after today's final round -- as long as Nick Dougherty doesn't finish third or higher.
Dougherty shot 69 on Saturday and is tied for 23rd place, six shots off Gregory Havret's lead.
"I do think I need to win, but it is feasible and it would be a wonderful way to make the team," Dougherty said. "Ollie's the favorite, but I'll see if I can make him sweat a little."
Wilson was happy to make the cut, with an eagle and two birdies on the last 10 holes Friday.
He opened with 76 and is now tied for 52nd place.
Colin Montgomerie appeared to have lost his chance of a Ryder Cup wild card after shooting 76, falling into a tie for 54th.
Montgomerie, who has never lost a singles match in his eight Ryder Cup appearances, had little to say after his round.
"I think you've got plenty out of me this week, thank you very much," Montgomerie said.
Havret birdied the last hole for 69 to take a one-stroke lead over Anthony Wall.
Havret, whose last European Tour victory was in Scotland at Loch Lomond last year, had an eagle and four birdies at the five par-5s and finished at 11-under 208.
He had a bogey at No. 13 and a double-bogey at No. 15.
Wall (65) birdied seven of the last eight holes, including six in a row from the 11th. He's one shot ahead of five players -- Marcel Siem (66), Lee Westwood (66), Ricardo Gonzalez (67), David Howell (68) and Soren Hansen (68).
Darren Clarke shot par 73, including a four-putt, double-bogey 7 at the long 12th. Now in 38th place, Clarke must rely on his second victory of the year at the Dutch Open last week to entice captain Nick Faldo into awarding him a wild card.