Armed with an offer that no else in the NBA can make – a chance to partner with Carmelo Anthony on an instant championship contender – the Phoenix Suns are planning an aggressive pursuit of LeBron James on Tuesday, league sources told Yahoo Sports.

Suns officials understand the bid will be something of a long shot, but are determined to get a meeting with James to convince him how the possibilities of two full max contracts, a roster stocked with talented, young players and the chance to pick the superstar free-agent partner of his choice ought to make Phoenix one of his most appealing suitors.

Phoenix is determined to emerge as a legitimate destination for James and Anthony, who have privately shared an affinity for playing with each other in the NBA. Salary-cap structures make it prohibitive for teams elsewhere to fit these two stars together without completely gutting a roster, but Phoenix's general manager Ryan McDonough has constructed a far different reality to sell them in potential meetings next week, league sources told Yahoo Sports.

The Suns have $33.5 million in salary-cap space and could shed the next $10 million needed to sign James and Anthony to maximum contracts without unloading the young core of guards Eric Bledsoe and Goran Dragic and center Miles Plumlee that pushed the franchise to 48 victories in the Western Conference last season.

View photos LeBron James' agent also represents Suns guard Eric Bledsoe. (AP) More

The Suns drafted North Carolina State's T.J. Warren, a scoring forward, Syracuse guard Tyler Ennis and Serbian scorer Bogdan Bogdanovich in the first round of Thursday's NBA draft.

Within hours of free agency starting on Tuesday, James ($20.7 million) and Anthony ($22.4 million) have max contract starting salaries that are easily reachable for the Suns. The Suns' flexibility allows for James to pick any free agent – this summer or next – for himself. It could be Anthony or Chris Bosh this summer, Kevin Love next summer.

The Suns have three first-round draft picks in 2015, and the picks could help the shape the roster with deals for veteran players, or infuse more young talent – or both – based on whatever intrigues the best player on the planet.

For now, the Suns are like everyone else in the NBA, including Houston and Cleveland: hoping against hope James will pause before recommitting to a deal with the Heat and truly bring an open mind to free agency. So far, James' representatives have been cautious on promising meetings with teams, and Heat president Pat Riley has been working on new deals with the reps for the four players who've opted-out of Miami – James, Bosh, Dwyane Wade and Udonis Haslem – sources said.

The Suns are banking on James' basketball acumen and business intelligence to see the roster, financial flexibility that could sustain the Suns' success for years. Phoenix officials believe the best chance to get Anthony away from his preferred free-agent destinations – Chicago and Houston – will be to turn James' attention toward the Suns, and get Anthony on board with his one true chance to play with James, sources said.

The Suns plan to pursue meetings with James and Anthony – or Bosh, if that's the direction that interests James. James' agent Rich Paul also represents Bledsoe, who is a restricted free agent this summer. Phoenix plans to aggressively pursue re-signing Bledsoe or match any offer sheet for him, sources said.

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