NEW YORK -- Frank Francisco's time as Mets closer could be coming to an end, if the team's interest in adding another established ninth-inning man to its bullpen is any indication.

Despite signing veteran relievers Scott Atchison and LaTroy Hawkins to Minor League deals earlier this week, the Mets are not done adding bullpen help, according to a source. General manager Sandy Alderson has made no secret all winter that he would like to add at least one veteran reliever on a Major League deal, and several intriguing options still remain available.

Chief among them is Jose Valverde, the former Tigers closer who lost his ninth-inning duties during Detroit's World Series run last season. The Tigers did not make any serious attempt to re-sign Valverde, 33, who saved 35 games in 40 chances with a 3.78 ERA last season.

Statistically speaking, it was his worst season in years. Valverde has saved 277 games over a largely successful 10-year career with the D-backs, Astros and Tigers, posting a 3.11 lifetime ERA with more than a strikeout per inning.

The Mets are also still gauging the health of Brian Wilson, scheduling a second visit to watch the former Giants closer pitch. Whether the Mets sign Wilson depends in large part upon how they assess his recovery from Tommy John surgery. But in a telephone interview last week, Alderson confirmed the team's continued interest.

Brandon Lyon, whose checkered career includes ninth-inning duties in Arizona and Houston, is also available. As is Francisco Rodriguez, who served as the Mets' closer from 2009-11.

Still only 31 years old, Rodriguez could help the Mets if he is willing to accept a significant decrease from the $8 million he made last season -- and if the Mets are willing to accept the public relations hit. Francisco is still infamous in New York for assaulting his girlfriend's father following a 2010 game at Citi Field.

Rodriguez and Valverde are both represented by agent Scott Boras, who is notorious for extracting top deals for his clients. But the Mets have made it clear that they are not going to overpay for bullpen help.

Still, at this late juncture of the offseason, compromise may be possible. One team insider pointed to Kyle Farnsworth's recent deal with the Rays as a signal that the market for relief pitchers has softened considerably since the beginning of the winter. Farnsworth, a former closer, can make no more than $3 million through base salary and incentives.

"There are still a bunch of names out there," the insider said, indicating his club's preference to acquire one big name as opposed to two lesser ones. "The value now with the Farnsworth signing, it's obviously changed considerably from where it was earlier in the winter. There are still several -- maybe even more than that -- guys that we think can help us at the back of the bullpen."

If the Mets sign even one of them, it could spell the end of Francisco's time as closer. Alderson has made it abundantly clear in recent weeks that he is not committed to his incumbent ninth-inning man, who still has one year and $6 million remaining on his contract. Francisco fell out of favor with the organization after posting a 5.53 ERA in 48 appearances last year, then underwent surgery after the season to remove a bone spur from his right elbow.

Speaking on SNY's Hot Stove show Thursday evening, Alderson said he is not "terribly comfortable" with the idea of Francisco as his Opening Day closer.

"Coming out of last season, looking with what Frankie has been dealing with in the offseason as far as his elbow is concerned, I don't know that we could have a lot of confidence in where we are," Alderson said. "I hope that Frankie is able to step up. We've taken a lot of the time to look at other possibilities and ways that we can shore this up. At this point, we have added some pitching, but more at the front end of the bullpen as opposed to the back end.

"I think we're going to have another guy or two between now and Spring Training. Now whether it's a back-end guy that will really compete with Frankie, or whether Frankie is the guy going in and the competition comes from Bobby Parnell or someone else, who knows? We'll just have to see."