Odom and Ariza become unrestricted free agents on July 1.
"You want to keep the team together," Odom said Thursday. "We just won a championship, you don't want to see one piece not there. Hopefully we can keep everybody here."
Odom met with coach Phil Jackson and general manager Mitch Kupchak during an individual 20-minute exit interview.
"Hopefully, it won't take that long," he said, joking about upcoming contract negotiations. "In and out, three years, 80 million."
In between player interviews, Jackson took a congratulatory call from President Barack Obama. A visit to the White House by the Lakers is under discussion, a team spokesman said.
Kobe Bryant, MVP of the finals, can terminate the last two years of his contract and become an unrestricted free agent next month. His exit interview is set for Friday.
Odom, who turns 30 in November, played a key role off the bench in the Lakers' run to their 15th NBA championship. He averaged 12.3 points and 9.1 rebounds during the playoffs. He made $14.1 million this season.
In a downtrodden economy, this summer's free agent market could see fewer offers and less money being offered by teams. That might make it possible for the Lakers to bring back both Odom and Ariza, who made a case for a significant raise with his defense on Orlando's Hedo Turkoglu in the finals.
Ariza averaged 11.3 points, 4.2 rebounds and 2.3 assists in the playoffs, and earned $3.1 million this season. A day earlier, he said he wants to return to his hometown team.
"It's always difficult, especially the economic times we're in now," Odom said. "I got to make a decision that is best for my family. At this point in my career, I owned a home, I owned a car, done pretty well. Everything I do now is for them and their kids. It's my time to pay that back to my family."
Odom said he wouldn't be swayed by another team offering him a starting spot.
"I won my first championship coming off the bench, that doesn't make a difference," he said.
If he returns, Odom said he anticipates playing more minutes at point guard and small forward while rebounding more.
Jackson and Kupchak encouraged Odom to stay in shape and hit the weights during the offseason, which he took as a sign the team wants him back. At the same time, in a nod to his social life, they urged restraint.
"We won a championship, I'm 29, decent looking," he said, smiling. "When we go out, I'm well-received, so they want me to take care of myself.
"I go out to a restaurant, everyone stands up and claps, go to the supermarket and everyone starts clapping."
Like Odom and Ariza, high-jumping reserve guard Shannon Brown becomes an unrestricted free agent five months after coming from Charlotte in a trade. He averaged 4.9 points and 1.2 rebounds in the playoffs, getting his most minutes against Houston in the Western Conference semifinals that went seven games.
"I think they're very interested in bringing me back, I want to be back," he said. "It's real important. Got another chance to win another championship and continue to get better. With this group of guys we got, the sky's the limit how good we can be."