What is next Baby step?

But even with all the good tidings, Big Baby and the Celtics know that anything can happen once free agency begins Wednesday.

“I’m eager and kind of curious,’’ said Davis. “I don’t know where I’m going to be. I like security. Not knowing where I’m going to be is scary. But at the end of the day, I’m in a good position where I’m going to make more money.

“I’ll be very excited to come back to the Celtics or go to a team where I might start. Wherever I’m at, I’ll be happy.’’

The Baton Rouge native averaged 4.5 points and 3 rebounds as a rookie during the 2007-08 season, but was told he needed to lose weight and improve his mid-range jumper. In his second season, a little lighter Davis averaged 7 points and 4 rebounds in 21.5 minutes per game and hit his mid-range jumper regularly. In 16 games as a starter, the 23-year-old averaged 12.6 points and 5.6 rebounds in 33 minutes per game.

Davis showcased himself in the postseason, averaging 15.8 points and 5.6 rebounds. His highlight came when he nailed a game-winning jumper at the buzzer in Game 4 of the second-round series against Orlando.

His postseason play, said Davis, “helped me a lot in showing I can be a player in this league, competitive and a force.’’

So would he prefer to be a starter now?

“If I’m on a team where it’s tough to get wins, a young team, I’d love to start,’’ said Davis, who made $711,517 last season. “But if it’s a championship-caliber team, I’d love to come off the bench. It depends on where I am. I’d love to come off the bench behind KG. But if not, I’d love to start, too.’’

Celtics president Danny Ainge has said a qualifying offer will be made to Davis Tuesday to ensure that he will be a restricted free agent, which gives Boston seven days to match any offer sheet. Davis is a free agent in a tough economy with a lot of unrestricted big men available.

One NBA general manager said Davis could maybe garner a contract paying $3 million-$4 million in the first year, while another said he’d get close to the mid-level exception (at least $5.6 million). Teams eyeing Davis also know that Boston is keenly interested, too, with matching power. But the Celtics are also over the projected luxury-tax threshold by nearly $2 million.

“We like Glen, but we’ll just have to see how it goes,’’ Ainge said.

Davis has been working out daily in Houston for about a month now, doing basketball drills, conditioning, and Muay Tai boxing. He says he has dropped from 320 pounds at the end of last season to 300 and believes he can get down to 270.

Davis also said he is working hard to be a consistent shooter from 3-point range. Furthermore, he has been selected to take part in USA Basketball’s minicamp for future prospects next month in Las Vegas.

“I’ve been working out, eating right, doing Muay Tai,’’ Davis said. “I’m doing real kickboxing like the real guys do. That’s what is getting the weight off.’’

Losing Davis could hurt the Celtics the way James Posey’s departure did last year. The good news for Boston is that Davis and the Celtics want to stay together. The bad news is that it’s all business once free agency arrives.

“It’s hard,’’ said Davis. “It’s where you started your career. It’s where it all began. But at the end of the day, it’s a business and you know that in the back of your mind.’’

Putting the 'free' into free agency

Last season, NBAPA deputy counsel Hal Biagas worked out a buyout with the Knicks on the final year of Marbury’s contract, worth $20.8 million, that cost him $1.5 million-$2 million. He signed with the Celtics shortly thereafter for $1.3 million for the remainder of the season and did not have to pay the NBAPA commission.

Because things went well with Biagas, Marbury is expected to stick with him. Biagas said he had no problems with helping him again.

“The best thing about the NBAPA is that they work for you for free,’’ said Marbury via e-mail. “When you have a team that negotiates the Collective Bargaining Agreement for all the players representing you, there is strength in numbers.’’

Etc.

1. Rasheed Wallace, Pistons, PF-C, unrestricted. Fiery yet talented vet who plays inside and outside and has championship experience. Has mutual respect with Garnett and would come off bench.

2. Grant Hill, Suns, SF, unrestricted. Played for Doc Rivers in Orlando and seems to have overcome his injury woes. Could be attractive as Paul Pierce and Ray Allen’s backup.

3. Anthony Parker, Raptors, SF, unrestricted. Brother of WNBA star Candace Parker could fulfill Rivers’s hopes of getting a solid backup for Pierce. Can play shooting guard, slashes, and has a solid jumper.

4. Chris Andersen, Nuggets, C, unrestricted. Wanted to be a Celtic last year, but Patrick O’Bryant was signed instead. The Nuggets are hopeful of re-signing “The Birdman,’’ who is marrying a Denver girl.

5. Antonio McDyess, Pistons, PF-C, unrestricted. Has a solid relationship with Ainge, but is very comfortable in Detroit and isn’t much for change at this point in his career.

6. Drew Gooden, Spurs, PF, unrestricted. If he had been bought out earlier in Sacramento, he could have ended up in Boston. Still has good relationship with Rivers, his coach in Orlando.

7. Joe Smith, Cavaliers, PF-C, unrestricted. Celtics had some interest in him before signing Moore last season. Played with Garnett in Minnesota and could add scoring off bench.

8. Fabricio Oberto, Pistons, PF-C, expected buyout. Could be a solid addition at both post spots off bench and a fill-in starter when needed. Smart player who has a reliable mid-range jumper.

9. Bruce Bowen, Milwaukee, SF, expected buyout. Word is he would love to go to the Magic. Don’t expect San Antonio to try to re-sign him. Would be solid veteran backup for Pierce with championship experience.

10. Linas Kleiza, Nuggets, SF-PF, restricted. Very versatile forward who can score in post and hit perimeter shots. Could be a good backup for Pierce, as he has been for Carmelo Anthony in Denver.

Marc J. Spears can be reached at mspears@globe.com