The Miami Heat went after Chauncey Billups before last season but weren’t able to get him. They soon will have another chance.

The veteran point guard will become a free agent July 1. He said he then will consider the Heat.

“Of course, I would have interest in Miami, of course,’’ Billups told FOX Sports Florida after having received the NBA’s inaugural Twyman-Stokes Teammate of the Year Award prior to Sunday night’s Game 2 of the NBA Finals at AmericanAirlines Arena.

The Heat went after Billups after he was released in December 2011 as part of the NBA’s amnesty provision. However, the Los Angeles Clippers won the bidding process, and he has played with them the past two seasons.

But Billups, 36, said he will look at all options this summer. He was asked if the Clippers have any sort of inside track to re-sign him.

“I’m wide open,’’ Billups said. “Free agent means free.’’

It remains to be seen if the Heat, who are pleased with young point guards Mario Chalmers and Norris Cole, might be willing to bring in a veteran at the position. But Billups said he’s been watching the Heat and believes he could be an asset.

“Absolutely, I could help them,’’ Billups said before the Heat faced San Antonio after having lost the Finals opener last Thursday

Billups averaged 15.0 points for the Clippers in 20 games in 2011-12 before suffering a season-ending torn Achilles tendon. He continued to be hampered by the injury last season, missing 38 of the first 41 games.