The Houston Rockets have ramped up their pursuit of Chris Bosh and are, in the words of one source, "heavily engaged" in trying to convince the All-Star power forward to leave the Miami Heat in free agency.

Sources close to the process told ESPN.com on Sunday that the Rockets -- though they haven't formally been told they are no longer in the running for top free-agent target Carmelo Anthony -- have intensified their pursuit of Bosh over the weekend in the hope that LeBron James will seriously consider leaving the Heat.

Sources say the Rockets have ramped up their pursuit of Chris Bosh in the hopes of pairing him with their current All-Star big man, Dwight Howard. Christopher Trotman/Getty Images

Bosh is resolved to wait on James to make a decision before he makes a decision on any other offers, as his preference remains to return to Miami with James, according to a source. However, the longer the process has gone on, the more Bosh has felt compelled to explore "Plan Bs," the source said.

Miami has remained a favorite to re-sign Bosh, even if it required him to take a pay cut from last season's $19 million salary.

Yet, as ESPN.com first reported Thursday, Houston has been plotting to shift its focus to trying to swipe Bosh from the Heat and convince the Texas native to return to his home state as soon as the Rockets felt like Anthony was out of reach.

Sources say Bosh remains willing to take slightly less than his value on the open market to return to the Heat if James and Dwyane Wade are also coming back and if Heat president Pat Riley can upgrade the current roster. But nearly a week into free agency -- with James' agent Rich Paul having opened negotiations with a handful of rival teams and Riley having secured no free-agent commitments -- sources say Bosh has felt compelled to consider other options himself.

"They appreciate what they've done in Miami those four years together, and they want to make sure they have a chance to have that same success the next four (years)," Henry Thomas, agent for Bosh and Wade, told ESPN.com's Michael Wallace on Sunday at the Orlando Pro Summer League. "With Dwyane, he's been there his entire career, so he's in a unique situation. Chris has made it known how he's felt about being in Miami these four years."

James, Wade and Bosh each opted out of the final two years and more than $40 million left on their respective contracts last month to become free agents.

The moves, in addition to other expiring contracts and options held by Miami's other players, gave the Heat at least $50 million in cap space and flexibility for Riley to retool the roster in free agency. Riley and coach Erik Spoelstra have traveled the country in recent days on a tour of free-agent meetings with Pau Gasol, Trevor Ariza, Luol Deng and Marvin Williams, among others. The Heat appear to have set a priority on adding perimeter depth behind James and Wade and also to upgrade the power forward rotation.

Thomas insisted that Bosh and Wade are operating under separate circumstances, but expects them to reach decisions on new deals "within the next couple of days."

Sources say Bosh would expect a four-year maximum offer of $96 million to leave Miami for Houston or any other suitor.

ESPN's Chris Broussard reported Wednesday that Bosh was seeking a five-year deal worth between $80 to $90 million to re-sign with Miami, while Wade is thinking along the lines of $55-60 million over four years.