Brown signed a one-year deal worth a reported $15million after he was released by the Oakland Raiders on Saturday following a tumultuous offseason.
The 31-year-old had 104 receptions for 1,297 yards with an NFL-leading 15 touchdowns last season for the Pittsburgh Steelers, and was traded to the Raiders in March.
Defending Super Bowl champions New England travel to Florida to face the Miami Dolphins on Sunday, though Belichick is uncertain if Brown will feature.
"You know, I don't know," Belichick said in a news conference.
"We just acquired him yesterday. We haven't practiced so I can't answer that question now. We'll take it day by day and see how it goes.
"We think he'll help our team. Until we start working with him, part of that is actually having a hands-on opportunity to work with a player and see exactly how everything fits together and what we can develop. We'll just see how that goes."
Brown's spells in Pittsburgh and Oakland have been marred by controversy, but Pats quarterback Tom Brady is optimistic the Patriots' latest addition will not pull similar stunts in New England.
"You don't judge anything," Brady said in a radio interview with Westwood One's Jim Gray.
"I'm not judging anything before I've had a chance to go out and practice and prepare. You know, Antonio, meeting him I really enjoyed being around him, he's a very smart football player, knows how to play the game. He's been extremely productive."
Brady also revealed he will hold regular meetings with Brown as he looks to build a fruitful relationship.
"The only thing that I know what we can do is to go out there and work at it to meet and to communicate and get on the practice field and go through things," Brady added. "I'm not buying into any hype or potential. I'm into work.
"We're going to meet as much as we possibly can. I think that the quarterback-receiver relationship is so important. The more you know each other, the more you know what each other are thinking, the faster you can accelerate the trust and confidence in one another when you get on the field.
"But, when you haven't played with guys, you have to try and do it as quickly as possible. The clock is ticking on us right now. This is not the offseason program.
"This is about real games that count, and we're going to try and spend as much time as we can together and really get up to speed and talking with what our roles and responsibilities are."