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.

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.