However, the door remains open for Ludwick to return to the Reds.
"He wants more than one year," Reds general manager Walt Jocketty said. "I talked to his agent last night and will talk again with him next week. Hopefully, we'll get something worked out."
Ideally, Jocketty said, the club hopes Ludwick will accept a two-year contract.
Back in January, Ludwick signed a one-year, $2.5 million contract as a free agent that carried a $500,000 buyout option.
The deal was a relative bargain, as Ludwick had struggled for much of 2010 and 2011. He used his one season with the Reds to revive his numbers, hitting .275 with a .531 slugging percentage, 26 home runs and 80 RBIs in 125 games.
Ludwick, 34, also became a veteran leader in the clubhouse and was a big part of the club's successful National League Central-winning season. His contributions were most vital while Joey Votto was injured.
In 43 games while Votto was on the disabled list, Ludwick hit .340 with 12 homers, 36 RBIs and a 1.051 on-base-plus-slugging percentage.
As expected, the Reds also declined the $11 million mutual option for closer Ryan Madson after he missed all of 2012 with an elbow injury that required Tommy John surgery. Madson, who was signed as a free agent in January to a one-year contract in worth $6 million, got a $2.5 million buyout and becomes a free agent. He saved 32 games for the Phillies in 2011, but was injured during Spring Training for the Reds.
Jocketty is also open to bringing back Madson as well as free-agent catcher Dioner Navarro and reliever Jonathan Broxton.
"We've had discussions with all of them today to see if we can work," Jocketty said. "I don't know if we'll get to sign all of them. They all expressed interest in coming back."