The Knicks have an offer on the table for 6-foot-8 Orlando combo forward Mario Hezonja for a portion of the $8.6 million, mid-level exception on a one-year deal, according to an NBA source.

The sharpshooting Hezonja was seeking a multi-year deal, but if he settles, the Knicks’ Michael Beasley era likely would be over.

The Knicks still are keeping tabs on veteran power forward Anthony Tolliver as president Steve Mills, general manager Scott Perry and coach David Fizdale all have talked to him since free agency began, Sunday at midnight, according to a source. Tolliver, too, is looking for multiple years and has a handful of suitors, including Dallas and the Clippers.

The Knicks want to strategically use a small part of their mid-level exception also to sign project center Mitchell Robinson, their second-round pick.

According to a source, the Knicks are also involved in trade talks early in free agency, possibly taking steps to dump Courtney Lee’s salary.

Hezonja, a 23-year-old from Croatia, finished the season shooting a subpar 33.7 percent from 3-point land despite a second-half surge. He’s a career 33.2 percent 3-point shooter and has struggled with quickness on defense — which is why some scouts think he might be better as a small-ball power forward guarding slower players.

One NBA scout called him “a tease.’’

“Hezonja is an enigma to me,’’ another scout said. “He looked promising as a rookie only to regress until the second part of this past season. He looked awful the first half. Poor instincts, didn’t shoot it well. The second part, a light came on for a bit. But he’ll wind up being suited as a small stretch 4 versus his natural position at 3. His youth makes him worth a flier, as he can shoot and still has development potential.”

The new Magic brass elected not to extend him a qualifying offer, making him an unrestricted free agent.

Perry may feel he already has skin in the game. As an Orlando executive, Perry was part of the decision-making process to select Hezonja, who was drafted No. 5 overall in 2015 and was headed to lottery-draft bustdom before last year’s uptick. A section of the Knicks’ front office still had reservations about Hezonja’s staying power.

If Hezonja accepts, the Knicks — as Kristaps Porzingis heals from knee surgery — could attempt to plug in another stopgap power forward with their biannual exception. They reportedly reached out to Trevor Booker and Amir Johnson. Beasley still could be signed for the $3.2 million non-Bird exception.

Tolliver, though, is high on their list.

“Tolliver is a good floor-spacing backup 4,’’ an NBA scout said. “He can start in a pinch but is best playing 20 minutes. He is a team guy, plays hard, good 3-point shooter and a solid, not great defender. He always gives effort.”

The Athletic reported Saturday night the Knicks reached out to Hezonja and have spoken to him. ESPN reported mutual interest. It’s unclear how Hezonja would fit into the long-term plans.

Signing Hezonja would make it easier for the Knicks to trade Lee — or even use the stretch provision on Sept. 1 that would save another $8 million in 2019 cap space. That gets them closer to being able to consider a Porzingis contract extension by the fall. The Knicks don’t want the extension to ruin their chance of having space for a maximum-salary free agent in 2019 with Kyrie Irving, Kevin Durant, Klay Thompson and Kawhi Leonard expected to headline the field.