A senior tour "rookie" at age 50, Allan matched Cink's six-under-par 66 in Grand Blanc, Michigan on Saturday to be three shots behind the American leader, who was at 11 under.
Wins have been few and far between in Allan's long pro tour career but he does boast a European tour victory at the 1998 German Open to go with his 2002 Australian Open title at home.
Allan was tied with American David Branshaw (69) and South Korean star K.J. Choi (70) with fellow Australian Rod Pampling (70) in the group a shot further back .
He had seven birdies against a single bogey and was asked about his strategy going into Sunday.
"You've just got to play well," Allan said. "If I go out and try too hard for birdies early, it ends up in disaster, so I just try to let the round play out.
"We don't need to birdie the first few holes to have a good round. You can build into the round and have a hot finish, too.
"I'm just going to go out there and try and play well."
Fellow Australians Mark Hensby (66, tied 9th at five under) was also well placed along with David Bransdon (68) and Greg Chalmers (72) who were at four under.
The 51-year-old Cink has four top-10 finishes this season but no career wins on the PGA Tour Champions.
"Golf is just a funny game, and it can just leave you in a hurry," Cink said. "I'm aware of that. It's going to take a lot of discipline, a lot of patience and really just being true to who I am and how I play tomorrow to get this thing done. But I'm looking forward to the challenge."
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