WALTHAM, Mass. -- Boston Celtics forward/center Chris Wilcox will miss nearly a month with an ulnar collateral sprain in his right thumb, according to coach Doc Rivers.

Wilcox injured the thumb on Tuesday in Chicago and has sat out the last two games, though Rivers had admitted he was going to lean on other bigs given Wilcox's recent defensive struggles. Now the injury will keep him on the shelf.

"Chris is out; he’s out for a while," Rivers said after the team's practice on Sunday. "I don’t know how long, but the first report I got was three to four weeks."

With Wilcox injured and the departure of Darko Milicic earlier this season, the Celtics are thin yet again at the center position and have been forced to lean on undersized big men like Brandon Bass and rookie Jared Sullinger. Rivers was asked if the team needed to make a move for a big man.

"You would think, but obviously that’s the one position where they don’t grow on trees. They actually grow," quipped Rivers. "We just have to be patient. Obviously, we need another big with Chris being out. I don’t know if we’re going to get another big on this trip."

The Celtics could attempt to muddle through until Jan. 7 when free agents are eligible to be inked to 10-day contracts. That would afford Boston a chance to add a player to Milicic's vacated spot without forcing a move that clogs a roster spot for the remainder of the season, leaving the team able to still be active at the trade and waiver deadlines when the players available might be glitzier.

And what about rookie Fab Melo, who set a D-League record with 14 blocks as part of a triple-double effort on Saturday in Maine?

"I haven’t talked to anyone that thinks he’s ready to come up yet," said Rivers. "There might be your answer."

The Celtics dressed only 10 bodies for Friday's overtime loss to the Milwaukee Bucks. Leandro Barbosa missed that game due to a personal matter and will not be with the team on Christmas Day in Brooklyn (he is expected to rejoin the squad in Los Angeles for the final three games of that road trip).

Avery Bradley is nearing a return after enduring double shoulder surgery, and Rivers didn't rule out the possibility of him debuting on this road trip, but said he didn't want to pressure the training staff. Bradley had been eyeing a return on Jan. 2 when the team returns home, but had planned to travel on the road trip.

"I think there’s a chance [he'll play on the trip], but I don’t know what the chances are," said Rivers. "I haven’t talked to anybody. The fact that he went through, again, today’s practice great ... I don’t know, I just try to stay out of that. Because he’s close and I don’t want anyone feeling like I’m pressuring them -- Avery or, more importantly, the doctors. Because Avery wants to play. I guarantee he wants to play the next game. But that’s something that I try to stay away from."

Rivers was asked if Bradley appeared game ready from what he'd seen in practice.

"He could play, there’s no doubt," said Rivers. "He’s ready to play. I don’t know about the healing part of it. Does it take those extra two weeks? He had two surgeries, and I think that’s what we forget. The first surgery was on one day, the second one was a lot later. And that’s the shoulder that still needs to heal. Now, if you can go through a practice, the way we’ve gone, especially today, can he play in a game? He might be able to. But maybe it’s still too early. I don’t know the answer."