MIAMI -- Seven-time All-Star center Alonzo Mourning said Wednesday night he already has "four or five good deals" on the table and expects to make a decision on July 16, the first day of the NBA's free-agent signing period.

Apparently, though, the Miami Heat are not one of the teams offering a good deal. Mourning has dismissed the contract offer made by his former team on Wednesday, calling it "not a significant one."

"They kind of made an offer. I can see them making a counteroffer," Mourning said.

Mourning hasn't ruled out returning to the Heat, but said he will look elsewhere if the team is committed to a lengthy rebuilding project. Mourning indicated that he and coach Pat Riley are headed in much different philosophical directions.

"I want to be here. But I understand Riles has to make the right decision for this franchise," Mourning said. "He's already explained to me that he has to rebuild, and I told him I want to win. That pretty much explains itself there."

Riley, addressing reporters in Orlando, where Miami has a team in a summer league, reiterated that he wants Mourning to remain with the Heat, who have paid him $105 million over the past seven years -- including his full $20.6 million last season when he sat out because of kidney disease.

"He's the heart and soul of this franchise and always has been. I want him to reboot it with me," Riley said. "He's going to have to cooperate with me but I can't expect him to do that. I know exactly where Zo is coming from and he knows exactly where we're coming from."

The Heat went 25-57 last season, the fourth-worst record in the NBA. Riley said before last month's draft that the team was entering a rebuilding mode, one that actually began last Sept. 5, the day he learned Mourning's medical condition would prevent him from playing in 2002-03.

Mourning would rather play for a team trying to win a championship right away.

"It's not just about the money, man," Mourning said. "Obviously, I want to be paid for my services, but it's not just about the money. It's about winning, too."

Dallas and Denver have confirmed interest in signing Mourning. He said he has not made a decision, but will sign a contract on July 16.

Riley said it's up to Mourning to decide if his future is best-suited elsewhere.

"I want him to be part of this franchise," Riley said. "I just don't think that right now, it can be on his terms."

Mourning, 33, was diagnosed in October 2000 with focal segmental glomerulosclerosis, a kidney disease that can eventually require a transplant. He played in just the final 13 games for the Heat in 2000-01, but appeared in 75 games the following season.

Last September, shortly before training camp, Mourning was advised by doctors to skip the 2002-03 season because test results indicated his condition had worsened.

He has since received medical clearance for 2003-04.