reported in the KC
They next entered heated discussions with the Baltimore Orioles to acquire veteran right-hander Rodrigo Lopez.
The moves came after market forces appeared poised to push free-agent right-hander Gil Meche beyond their financial means and while they awaited a response from right-hander Miguel Batista on a three-year offer for $24 million.
"We're asking our fans to continue to be patient," general manager Dayton Moore said, "but I'm not asking them to be patient with us losing 100 games again next year.
"I'm not asking them to accept that, because we're not going to accept that. I can tell you that right now. I don't want to ever have a losing season again. Ever. It's not fun."
Bannister, 26, is expected to join a rotation that presently consists of Odalis Perez, Luke Hudson and Jorge De La Rosa.
Lopez, if acquired, would complete the five-man unit.
Bannister is the son of former Royals pitcher Floyd Bannister and opened last season in the Mets' rotation before suffering a hamstring injury. He spent much of the year rehabbing in the minors before returning late in the season.
The Royals are believed to have offered outfielder Reggie Sanders for Lopez, but the Orioles appear to prefer Emil Brown.
Lopez, 30, led the American League in losses last season in finishing 9-18 with a 5.90 ERA. But he was 51-40 during 2002-05 and won at least 14 games in three of those four seasons.
Lopez is eligible for arbitration after making $3.75 million in 2006.
Sanders, 39, batted .246 with 11 homers and 49 RBIs last season in 88 games before undergoing season-ending knee surgery last August. He is under contract next season for $5 million.
Brown, 30, batted .287 with 15 homers and a club-leading 81 RBIs in 147 games. He is eligible for arbitration after making $1.775 million in 2006.
Talks continued into the night at the Disney World resort hotel serving as host to baseball's annual winter meetings.
Bannister finished 2-1 with a 4.26 ERA in eight games for the Mets, including six starts. He entered last season ranked by Baseball America as the Mets' No. 6 prospect.
Burgos, 22, was 4-5 with a 5.52 ERA last season in 68 games and blew 12 of 30 save opportunities before losing the closer's job in late July.
The Mets are looking to replenish a bullpen weakened by the free-agent departures of Roberto Hernandez and Chad Bradford.
The Royals arrived at the winter meetings prepared to overpay the market in an effort to sign Meche and Batista.
"The guys we're going after," Moore said, "are guys who can be part of our long-term future. That's why we think it makes sense.
"We've got some guys in our system whom we believe will be able to help us in the next year or two, but we need to mix in some older guys."
The Royals appear locked in a cross-state battle with St. Louis for Batista, who was 11-8 with a 4.58 ERA last season in 34 games for Arizona. Sources indicate the Royals made the higher bid, but it's uncertain whether they are willing to go much higher.
The Royals didn't blink in their pursuit of Meche, 28, until the price threatened to move past $40 million for four seasons. Meche was 11-8 with a 4.48 ERA last season in 32 starts for Seattle and has won more than 11 games only once in his six-year career.
The Cubs are generally viewed as the front-runners for Meche, assuming they don't sign higher-profile pitchers, such as Jason Schmidt, to fill out their rotation. The Blue Jays are also making a strong push.
"We came here knowing it would be competitive," Moore said. "It comes down to supply and demand."
