Dickey underwent an MRI at the Hospital for Special Surgery.
"It's a day-to-day issue," Dickey said. "I'm optimistic. I feel like it's just a matter of managing the symptoms and I'll be out there."
To make room on the 25-man roster for Pagan and Thayer, the team optioned outfielder Fernando Martinez to Triple-A Buffalo and designated left-hander Pat Misch, who had been serving as the team's long reliever, for assignment.
Pagan, who had been on the disabled list since April 22, was in the lineup batting sixth on Friday night against the Philadelphia Phillies. He was 2-for-4, scored a run and had a stolen base in the Mets' 6-4 loss.
Pagan, 29, said before the game Friday that a recent MRI revealed that he had a stress fracture in his rib cage, not the oblique injury that was originally diagnosed and reported.
Pagan was hitting just .159 in 19 games played before the injury. He said on Friday that he's sorted out his problems at the plate during his minor league rehab stint, where he hit .226 (7-for-31) with one home run and two RBIs in eight games with Class A St. Lucie.
Dickey suffered the injury while trying to cover first base during the Mets' 9-3 loss to the Chicago Cubs on Thursday afternoon.
The knuckleballer wore a boot and used a crutch after the game.
"It's sore," Dickey said. "But it's probably 60 percent better than it was when I did it."
In 10 starts for the Mets this season, Dickey is 2-5 with a 4.50 ERA. The 36-year-old has allowed 72 hits in 60 innings.
Dickey will throw a bullpen on Sunday to see if he can make his next start.
Dickey was unsure if he'd need surgery at the end of the season to repair the partial tear.
Manager Terry Collins said the team has a contingency plan if Dickey cannot pitch, but would not reveal it.
The Mets' starting rotation has already been decimated by injuries. Right-hander Chris Young is out for the season with a torn anterior capsule in his right shoulder, while ace Johan Santana is not expected to return from shoulder surgery until July.
"I kind of froze," Dickey said Thursday. "And then when I saw Murphy go to get the ball it kind of took me by surprise and I started up again. And when I did I felt a real intense burning sensation in my heel and involuntarily just went down. ... It's like I stepped on a railroad tie upside down, like a spike."
Collins said there was a small piece of good news in the initial diagnosis by trainers.
"At first they thought it was an Achilles tendon," Collins said Thursday. "I guess that's fully intact, so that's not the issue."
"This is all new to me," Dickey said. "I've never had the sensation I had when I was out there."
David Wright, who has been on the disabled list since May 18 with a lower back stress fracture, returned to New York after a visit with noted back specialist Dr. Robert Watkins in Los Angeles earlier this week.
Collins said optimistically that Wright could return to the field in 10 days. The third baseman hadn't started baseball activities as of Thursday.
General manager Sandy Alderson did say, however, that it's "possible" that both could rejoin the team after its 10-game homestand, which concludes on June 5.
"Until they start engaging in that type of activity, we just can't set a timetable going forward," Alderson said. "I'm hopeful we'll be able to do that in three or four days for both of them. If we're able to do that, it's very possible they'd be able to be back by the end of this homestand."
Collins also said that Ike Davis' ankle injury continues to be "a little bit of an issue." Davis had trouble rehabbing the injury, and was originally placed on the disabled list on May 11.
The 30-year-old Thayer pitched in 20 games for the Bisons, compiling a 2-0 record with four saves and a 2.05 ERA.
The 22-year-old Martinez appeared in nine games with the Mets and hit .250 (5-for-20) with a home run and two RBIs after the team recalled him on May 12 from Triple-A Buffalo.
The 29-year-old Misch made six relief appearances out of the bullpen for the Mets, winning his only decision, with a 10.29 ERA.
Mike Mazzeo is a regular contributor to ESPNNewYork.com. ESPNNewYork.com's Ian Begley contributed to this report.