The club on Tuesday submitted an offer of $2.75 million, while Walker countered with his proposal of $3.95 million.
If the two sides are unable to resolve their differences, San Diego will have its first arbitration case since 1998.
There still are two weeks of negotiating time remaining before the hearings will be held Feb. 1-20, giving teams plenty of time to avoid a hearing. Of the 43 salary exchanges last year, only six eventually went to a hearing.
Walker, 33, is expected to play a backup role at three positions -- first, second and third base -- with the signing of second baseman Marcus Giles as a free agent.
Walker played 44 games with the Padres in 2006 after arriving at the trade deadline in a deal with the Chicago Cubs. He batted .282 for the Padres, .278 overall, with nine homers and 53 RBIs. He's a .289 career hitter.
The Padres' two other potential arbitration cases were settled when shortstop Khalil Greene agreed to a $2.25 million contract for 2007, and catcher Josh Bard accepted a $1.05 million deal.
Greene, whose salary was $405,000 last season, can make an additional $50,000 each for 550, 575 and 600 plate appearances. He also can earn $50,000 for making the All-Star team, $50,000 for winning a Gold Glove, $25,000 for winning a Silver Slugger Award, $50,000 for winning an LCS MVP award and $100,000 each for winning the league MVP or World Series MVP awards.
Bard has the same incentives for making the All-Star team and winning the Gold Glove and Silver Slugger awards and the MVP awards for the league, LCS and World Series. Both Greene and Bard also can earn $50,000 for finishing second in the MVP voting and $25,000 for third.
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.