Lebron James Network: Sources: Heat want Ray Allen

Updated: June 30, 2012, 11:14 AM ET

If the Miami Heat have it their way, they'll have a commitment from Ray Allen within hours of Sunday's start of free agency. The longer the process plays out, the less it may favor them.

The Heat, according to sources, have made Allen their prime offseason target and will pursue him strongly when free agency opens Sunday at 12:01 a.m. ET.

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They intend to offer him their $3 million mini-mid-level exception, a chance to win another title and significant playing time as they continue with the plan to play LeBron James as a power forward in the future. Heat players, including James and Dwyane Wade, have been publicly and privately recruiting Allen over the last month.

"We've got five or six guys earmarked (in free agency) so we'll see how it goes," Heat president Pat Riley said. "We want to find as much space as we can on the floor for Dwyane, LeBron and for Chris (Bosh) to be able to operate."

The team would prefer to swoop in and secure his services quickly for several reasons. The Heat cannot win a bidding war for Allen, so they're hoping the chance to play on a contender will make up for the below market value offer. Also they want to grab Allen before other suitors get their free-agent houses in order.

All Miami has to offer is that $3 million exception, a steep pay cut from the $10 million Allen earned last year. The Boston Celtics, who have cap space and Allen's Bird rights, could pay him significantly more. Yahoo! Sports recently reported the Phoenix Suns are expected to chase Allen and they could have more than $20 million in cap space. There will be other contenders as well.

Allen may want to wait and see how things play out. Multiple media outlets reported Saturday that Kevin Garnett is planning to return to the Celtics. However, the Celtics may need to deal with other free agents including Jeff Green before they see what they can offer Allen.

The Suns have to make a decision on what to do with Steve Nash before getting an offer together for Allen.

Allen could also wait to see where stars Deron Williams and Dwight Howard end up before making a final decision on where he might want to play. All of which has the Heat interested in moving as quickly as possible.

The Heat did handle some other free agent business over the weekend. Center Ronny Turiaf, who signed with the team in March, elected not to pick up his $1.1 million player option for next season by Saturday's deadline. He will be an unrestricted free agent. He played in 13 regular season games, averaging 3.5 points and 4.5 rebounds, and 12 playoff games, averaging 1.9 points and 2.6 rebounds, for the team.

"The option was an insurance policy in case he got hurt," agent Mark Bartelstein said. "He's interested in coming back but not at the minimum salary."