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Fred Couples did his part for the Champions Tour by showing up for the Encompass Championship, his first start since March. But Rocco Mediate wanted more.

So as Couples was killing time Thursday on the first tee box at North Shore Country Club, Mediate pushed in a stroller with daughter Francesca and said, “Hey, Freddie, can you babysit tonight?”

Couples chuckled and left the question unanswered.

The same goes for the questions surrounding the Champions Tour’s future in the Chicago area.

This weekend marks the third and final time Encompass Insurance, owned by Northbrook-based Allstate, will be the title sponsor. The Champions Tour is eager to find a new sponsor and would likely seek a new host, with the Glen Club, Cog Hill, the Merit Club, Chicago Highlands, Exmoor and Wynstone among the possibilities.

Glenview’s North Shore has been a terrific site, with players comparing the condition of its fairways to those at Augusta National. But as Champions Tour player Kenny Perry put it, half-jokingly: “I’m sure the membership is tired of us, and I can understand that. You’ve got a short window for golf in Chicago, and then you have to give up your golf course to us for a week.”

Dates will be available on next year’s Champions Tour calendar, even though Steve Stricker will host a new event in Madison, Wis., in June.

The challenge is getting a company to pony up the required $3 million to $4 million per year, rather than devoting its sports-marketing budget to the Bears, Bulls, Blackhawks, Cubs, White Sox or BMW Championship, which is in the Chicago area every other year.

“Some of the competition,” Encompass President Tom Ealy said, “blots out the sun.”

But Ealy could not be a bigger advocate for what a company can get for its sponsorship dollars, including pro-am slots, a driver-fitting exercise and small-group instruction from a pro such as Olin Browne.

“This tournament has delivered on everything we wanted,” he said. “The good news is we’ve got time. I still say ‘we’ because my job is to help find that next title sponsor. I can speak to it with great passion and credibility and talk about the (return on investment).”

But in many places, a Champions Tour stop is the big fish in a little pond. Here, the pond is Lake Michigan.

This year’s event moved from June to July to accommodate a U.S. Senior Open date change. That puts it up against a Sox-Cubs series and the PGA Tour’s John Deere Classic, three hours west in the Quad Cities area, where Jordan Spieth is tuning up for the British Open.

“Would I have preferred that we be unopposed? Of course,” Ealy said. “But I don’t think it will hurt in terms of the fans coming.”

Couples’ uber-cool presence doesn’t hurt. And spectators who came out the last two years witnessed outstanding finishes by major champions: Craig Stadler in 2013 and Tom Lehman last year made 12-foot putts on No. 18 to win.

The first two rounds Friday and Saturday feature celebrities, but the event got unlucky this year with late withdrawals from Roger Clemens, Johnny Bench and Craig T. Nelson.

That leaves six celebs to play in the final Encompass Championship: Brian Urlacher, Robbie Gould, Patrick Mannelly, Richard Dent, Jeremy Roenick and Mike Eruzione.

“It’s devastating to us to lose a tournament,” Perry said. “This is a great venue and Chicago’s a great city.”

The only potential benefit for Perry?

“My wife loves to shop downtown,” he said. “Spends way too much money here.”