"Can a 50-year-old win here? I think so. I'm one of them," said Couples, the 1992 champion whose silky smooth swing and laid back demeanor has made him a fan favorite.
"I'm not here just to play golf. I love the course and I would say my 71 is in pretty darn good shape."
Couples, 54, is playing in his 30th Masters and has played well at Augusta in recent years, leading some to wonder if he might be able to take over as the oldest Masters winner from Jack Nicklaus, who was 46 when he won his sixth in 1986.
The American has finished in the top 15 each of the last three years, holding the 36-hole lead in 2012 on his way to a tie for 12th, and he finished in sixth place in 2010.
In 29 Masters, the long-hitting Couples has registered 11 top-10 finishes.
It was also a strong day for Spanish veteran Miguel Angel Jimenez, 50, who made the turn at four under par before stalling at Amen Corner with a bogey at 11 and a double-bogey at the par-three 12th to join Couples on 71.
Scotsman Sandy Lyle, the 1988 winner, reached three under par by the fourth hole with three successive birdies before slipping back.
Twice winner Ben Crenshaw, 62, said he saw no reason why Couples could not remain in the chase.
"Fred loves this place. I wouldn't be surprised if he stays in there most of the week," Crenshaw, whose veteran magic deserted him on the way to an 11-over-par 83.
"And Jose is just one fascinating player. He hits the ball right in the middle of the club nearly every time. And he's a good thinker."
Couples, who won this year's Toshiba Classic for his 10th Champions Tour victory, admitted it was difficult to perform at a high level at Augusta after growing accustomed to senior tour competition.
"It's hard for me personally to play a course this hard day after day after day after day for four solid rounds," said Couples. "But my goal is to compete with these guys and not really worry about them.
"I'm happy with what I shot," said Couples, who bogeyed the 12th and the par-four 17th on the way in.
Couples, who has 15 career PGA Tour wins, the last coming at the 2003 Houston Open, said that if the likes of defending champion Adam Scott or young two-time majors winner Rory McIlroy play well he can not beat them, but he still held out hope.
"If I play well, I can compete with them and maybe with nine holes to go, I hit four unbelievable shots and do something good," said easy-going Couples with a grin.