Arbitration hearings will be held from Feb. 1-21, but the two sides still can reach an agreement up until the scheduled meeting.
Of the four, Zimmerman is the biggest name. He asked for $3.9 million, while Washington countered with $2.75 million. Zimmerman is coming off an injury-riddled season, playing in only 106 games because of left shoulder and right hand injuries. He hit .283 with 14 home runs and 51 RBIs.
Zimmerman and the Nationals have been trying to work out a multiyear deal since last Spring Training.
During that period, Washington vowed not to spend excessively, but the club was willing to give Zimmerman a contract similar to that of Rockies shortstop Troy Tulowitzki, who signed a six-year, $31 million deal in January 2008. Sources indicated then that Zimmerman wanted a larger contract.
Zimmerman's contract was renewed, and he made $465,000 in '08.
"The first three years is their time, and I guess the next three years is my time," Zimmerman said last October about the possibility of going to arbitration. "Ultimately I would like to sign a deal and be in D.C. It's just going to be a matter of whether the time is right and all the figures are right or stuff like that. It's an exciting time for me and hopefully for the Nationals, too."
Hill, Olsen and Willingham also are looking for pay raises. Hill, who made $402,000 last year, asked for $775,000, while the Nationals countered with $500,000. Hill missed most of the 2008 season due to an elbow injury.
Olsen, who came from the Marlins in the Emilio Bonifacio trade in November, is asking for $3.5 million, while the Nationals offered $2.5 million. Olsen was 8-11 with a 4.20 ERA in 33 games last year.
Willingham, who came with Olsen to Washington in the same deal, asked for $3.6 million, while the team countered with $2.55 million. Back problems forced Willingham to play in only 102 games last season. He hit .254 with 15 homers and 54 RBIs.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.