Francisco was sidelined at the end of last season with the same issue, then had a bone spur surgically removed in December after feeling a pinch and seeking a second opinion.
Mets manager Terry Collins said the inflammation Francisco suffered after throwing on flat ground last week in Port St. Lucie was not unexpected.
"I'm just dealing with the same stuff," Francisco said, alluding to last year's elbow issues. "I was playing catch. ... My inflammation hasn't gone down 100 percent. So they decided to shut it down for a little bit, until my inflammation goes down or my elbow gets better, so we can start a new program."
"Well, he's not throwing," Collins said. "We'll take a look at it. I talked to him last week. He did play catch. There was some inflammation in there. The training staff, they were prepared for it, for sure. They thought it might happen. So we just want to quiet the swelling down before he plays catch."
Collins said Francisco has certain benchmarks to achieve during spring training in terms of his throwing program to be ready for the season. Francisco already was on tenuous ground as the team's closer after posting a 5.53 ERA last season with the Mets.
"Frank told me last week, 'I'll be ready,'" Collins said. "[Pitching coach] Dan [Warthen] and I have kind of picked some dates that we think are going to be important so that we know he'll have the innings necessary to be ready for the season. If he meets those dates, I think he'll be on track. If he doesn't, we'll have to look in other directions."
Bobby Parnell would be the Mets' primary alternative for the closer role. Brandon Lyon also is in camp and is capable of closing out games. Collins said LaTroy Hawkins and Josh Edgin also would get ninth-inning looks in Grapefruit League games.
Francisco remains the most expensive free-agent signing in Sandy Alderson's three offseasons as Mets general manager. He is owed $6.5 million in 2013, in the second season of a two-year, $12 million deal.
Francisco said he feels like he remains the closer.
"It doesn't matter who you are and what you've done," he said. "There's always going to be competition. All those guys -- eighth inning, seventh inning -- they want to be the closer. ... I'm going to go out there and do what I've been doing. I'm not trying to do anything different. I'm going to get ready, be 100 percent as soon as I can and get people out.
"The boss, the 'jefes' and whatever, they're going to make the decision. And whatever they decide, I'm going to be OK with that."