The Houston Rockets, if they fail to land free agent Carmelo Anthony, plan to shift their attention to trying to swipe Chris Bosh from the Miami Heat, according to sources close to the process.

Sources told ESPN.com on Thursday night that the Rockets -- while still holding out hope that Anthony will choose them after hosting him Wednesday in Houston -- have already let Bosh know how interested they are in bringing the Dallas native back to Texas.

Thursday's revelations that LeBron James' agent, Rich Paul, has fielded pitches from multiple teams this week in Cleveland for James' services appear to at least raise the possibility that the Heat's star trio -- which also features Miami lifer Dwyane Wade -- might actually be breaking up.

The widespread assumption around the league, when free agency commenced Tuesday at 12:01 a.m. ET, was that James, Wade and Bosh had all but agreed to return to the Heat after hashing out new annual salaries among themselves.

Most league observers continue to believe that Heat president Pat Riley ultimately will convince all three Heat stars to re-up by next week, even if Bosh and Wade are forced to take pay cuts.

But sources say the Rockets are determined to test Bosh's resolve in the event Anthony elects to return to the New York Knicks or chooses one of his other three primary suitors this week: the Chicago Bulls, the Dallas Mavericks or the Los Angeles Lakers.

Houston needs a big forward with 3-point range such as Bosh in its search for the ideal frontcourt sidekick to All-Star center Dwight Howard. Sources say Bosh and Mavs star Dirk Nowitzki likely would have been at the top of the Rockets' list of free-agent targets had Houston believed it had a shot at either player.

Nowitzki committed Thursday to staying with the only team he has ever known for three more seasons, rebuffing Houston's attempts to recruit him, but the sudden uncertainty in Miami might give the Rockets an unexpected shot to try to tempt Bosh.

The Rockets have maintained for weeks that they could move the contracts of Omer Asik and Jeremy Lin to create enough salary-cap space to sign a high-priced free agent if they could get a commitment from one of the top names.

Houston then struck a trade with New Orleans to dispatch Asik to the Pelicans and now will try to get a commitment from Anthony or Bosh that necessitates Lin's exit.