The Chicago Bulls already took care of their biggest priority and concern on the first day of free agency by agreeing to pay shooting guard Jimmy Butler $95 million over five years, fighting off the likes of the Los Angeles Lakers and several others in contention to land the All-Star swingman. Bulls general manager Gar Forman also brought forward Mike Dunleavy back at a reasonable rate of $15 million over three years.

With those two key pieces returning to a squad that finished third in the Eastern Conference and went six games with the conference champion Cleveland Cavaliers in the second round of the playoffs, the Bulls can now turn to adding more depth and scoring in the back court.

According to the Chicago Sun-Times, the Bulls are interested in adding either Jeremy Lin or Rodney Stucky, citing each’s ability to play either guard role. The report also listed veterans Gary Neal and J.J. Barea as potential targets.

Chicago’s already stacked at point guard with former MVP Derrick Rose, Aaron Brooks and Kirk Hinrich returning, but the two-spot could need some sprucing up with little used reserves Tony Snell and E’Twaun Moore backing up Butler.

Thus Lin or Stuckey could be solid fits on the Bulls bench next season, assuming the Bulls can acquire either of them at the right price. Even though the salary cap ceiling is expected to rise to the neighborhood of $67 million, more or less, and the luxury tax threshold above $81.6 million, Chicago already has $61.7 million on the books for next season and so far that doesn’t include Butler or Dunleavy’s deal. There’s some room, but not so much that the Bulls can afford to overpay Lin or Stuckey without accruing massive tax penalties.

But at least in the case of Lin the Bulls could work out a reasonable deal. Due to his off-and-on shooting and defensive woes, the 26-year-old lost his starting spot to rookie Jordan Clarkson during his one season with the Lakers, making a back-up role with Lin’s next squad a possibility.

Under former head coach Tom Thibodeau Lin’s defense might have been an issue, but new coach Fred Hoiberg could ease up some of that emphasis on defense to allow his players more time and energy on the offensive end.

Thibodeau was also criticized for perhaps wearing his players down with too many minutes, and adding Lin or Stuckey allows the guard platoon to rest the injury-prone Rose and workhorse Butler for long stretches every night.

Averaging 4.8 assists for his career, Lin might better serve as a facilitator rather than a scorer for Chicago, especially with big men Pau Gasol and Taj Gibson able to get open in the paint. Lin however may have to take a pay cut after earning more than $8.3 million with L.A. last season.

But if Chicago’s simply seeking more scoring then Stuckey might the better choice. The 29-year-old improved his three-point shooting for a career-best 39 percent with the Indiana Pacers last season, and he’s shot 42.5 percent overall from the floor for 13.3 points per game over eight seasons.

Stuckey’s also largely come off the bench the last four years, and likely won’t have a problem doing the same in Chicago, whereas Lin could be seeking a starting or more regular sixth-man role. His contract demands should also be considerably lower than Lin’s, after Stuckey earned $1.2 million off a one-year deal with Indiana.