The right-hander signed a two-year, $10 million deal before the 2011 season and the D-backs hold an option for next year that includes a $1.5 million buyout.
Putz, 35, saved 45 games last year and had 27 entering Friday's game against the Dodgers.
"We have time to make that decision," D-backs general manager Kevin Towers said of picking up Putz's option. "He hasn't done anything performance-wise that would lead us to to believe that he wouldn't be here, but we don't have to make that decision right here today."
Proven closers have done well on the free-agent market over the past year. The Phillies signed Jonathan Papelbon to a four-year, $50 million deal during the offseason and the Marlins inked Heath Bell to a three-year, $27 million contract.
"Money is always an issue, but I think when you look at what other closers are signing for, the Heath Bells and stuff, $6 million [actually $6.5 million] for an experienced closer is probably not a bad number," Towers said. "He's been incredible, very consistent. The bullpen is a big part of our club, not only this year but going forward, and experience is important. A lot can happen in the next 30 days."
Putz, who makes his home in the Valley, made no secret of his desire to stay next year and beyond.
"I would love to finish my career in Arizona," Putz said. "I love everything about it here. Great organization, great teammates."
Before Friday, Putz had converted 18 straight saves and 21 of his last 22.