They also formally offered to Woody Williams in order to collect two compensatory draft choices, one from the Astros, who signed the veteran right-hander to a free-agent contract.
Along with Walker, Klesko and Park, Roberts -- reportedly close to signing a three-year deal with the San Francisco Giants -- has until Dec. 7 to accept or reject arbitration.
As Type A free agents, Roberts and Walker would command two compensatory picks each in the First-Year Player Draft if they are signed by another club.
Mike Piazza, Rudy Seanez, Doug Brocail, Shawn Estes and Sterling Hitchcock were not offered arbitration, making them free to negotiate deals without compensation involved. The club was undecided with regard to David Wells and Alan Embree as the 9 p.m. PT deadline approached.
"We'll know by Dec. 7 what they decide to do," Padres general manager Kevin Towers said of Roberts, Walker, Klesko and Park.
If they elect to accept arbitration and return to the Padres, Roberts and Walker would solve two of the club's pressing needs for a leadoff man and second baseman.
Park, if he returns, would be a candidate to retain his place in the starting rotation. He was a solid starter before intestinal bleeding forced him to undergo surgery in August, and he made a remarkable comeback to pitch in the postseason.
Klesko, who missed all but the final two weeks of the season after undergoing shoulder surgery, came back with force down the stretch. The veteran slugger could be a valuable bat off the bench or contend for the left-field job if Roberts signs with another club.
Towers was delighted to hammer out a deal with Blum, the 33-year-old infielder whose value to the 2006 National League West champions extended beyond his .254 average in 109 games with 17 doubles, four homers and 34 RBIs.
When Khalil Greene was rendered inoperative for most of the final two months with a hand injury, the versatile Blum -- who played all four infield positons for the club -- stepped in at shortstop and played commendably down the stretch.
Blum started at shortstop in the National League Division Series against eventual World Series champion St. Louis.
"We certainly wouldn't have gotten into the postseason without Blummer coming in and doing a great job at shortstop," Towers said. "He really came through for us.
"There's something to be said for Blummer being a good-luck charm. We made it to the postseason the last two years with him, and the White Sox [who acquired Blum at midseason in 2005] won the World Series with the guy coming through with a big home run [in Game 3 at Houston].
"He's a great guy in the clubhouse, a great guy to have on a ballclub with his versatility. He knows his role. He also led the league in pinch-hitting."
With 12 hits in 31 at-bats as a pinch-hitter, Blum led the Major Leagues with a .387 average.
As for Piazza, the team's regular catcher in 2006, the A's reportedly are considering him for the designated-hitter role vacated by Frank Thomas, who signed with Toronto. Philadelphia also is believed to have interest in Piazza, who still could return to the Padres as a free agent.
If Piazza does not return, Josh Bard and Rob Bowen are expected to share catching duties.
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.