"I'm optimistic that he'll be back," Bryant said Wednesday at a news conference in Singapore as part of a six-country Asian tour. "He makes us a much, much stronger team."
Negotiations broke down last week and the Lakers retracted a contract offer to Odom. The Miami Heat are also wooing the 6-foot-10 forward.
Odom played a key role off the bench in the Lakers' championship run, averaging 12.3 points and 9.1 rebounds during the playoffs.
Bryant said forward Ron Artest, who signed as a free agent with the Lakers earlier this month, will help bolster the team's chances to repeat as champions.
"I think Ron's going to be a great addition to us," Bryant said. "It's about how well we play together. No matter how much talent you have, it's about how you put those pieces of the puzzle together."
Bryant downplayed speculation that Lakers coach Phil Jackson may take some games off next season because of health problems.
"Who said he's coaching less?" Bryant said. "Phil likes messing with you guys. He'll be there all the time, unless he has a doctor's appointment to get to."
Bryant also said he was more likely to agree to play for Team USA at the world championships in 2010 and the 2012 London Olympics now that Duke coach Mike Krzyzewski has committed to lead the team.
Bryant and Krzyzewski won the gold medal as part of the U.S. men's team at the Beijing Olympics last year.
"I'm very excited to see that he signed on," Bryant said. "It influences all the guys just because we've been through that experience before and it becomes like a family."
"It definitely influences me."
"Just the hoopla that surrounds it and all the stories that would come out of it," Bryant said. "If that match up is to happen, we have to take it one day at a time, we can't get caught up in it being a given that we're going to be in the Finals.
"We have to take care of our business, but that being said, it would be a heck of a show."