Grateful Shved?

According to an NBA source, the Knicks are contemplating offering productive Russian combo guard Alexey Shved their $2.8 million room exception given to under-the-cap teams that have reached the cap benchmark.

Shved, appreciative the Knicks gave him a chance after a couple of rocky, unfulfilled seasons with Minnesota, Philadelphia and Houston, would probably accept it.

But he’s just one candidate. The Knicks are still shopping what is left of their money to spend this offseason — sans the minimum contracts they can offer. They have had talks with 35-year-old shooting guard Caron Butler, who finished last season with the Pistons after playing for the Bucks, and veteran shooting guard Willie Green, 33, who played for the Magic last season.

According to the source, Shved has two other NBA teams interested as well as a handful of European offers. Shved, 26, told The Post after last season he hoped to return to New York after grasping team president Phil Jackson’s triangle offense before suffering a broken rib in late March, ending his season.

With an ability to drive the ball, draw fouls and shoot from deep, the 6-foot-6 Russian averaged 14.8 points in 16 games and impressed Jackson immensely after he traded for him at February’s deadline, giving up Pablo Prigioni and a trade exception. The Rockets dealt the former Timberwolves draft pick because they feared he was headed back to Europe.

The Knicks need more scoring on a rebuilt roster that could resemble an expansion team, especially if fourth overall pick Kristaps Porzingis is not ready to produce as a 19-year-old rookie.

Jackson has added six players since the June 25 draft and has five roster spots left. But all their $28 million cap space is gone — spread among four role players, with the jewel being defensive center Robin Lopez. With stars shunning the Knicks, Jackson also signed serviceable shooting guard Arron Afflalo, young power forward Kyle O’Quinn and 2011 draft bust Derrick Williams.

Of the spots left, four could get filled by grinders from last season’s 17-65 squad and, no, Andrea Bargnani is not in the picture. Jackson had said he didn’t want to bring in “nine new players’’ and maintain some semblance of chemistry.

Ricky Ledo, the 22-year-old, 6-7 shooting guard, will be on the Knicks’ summer league team that debuts Saturday and has a small guarantee for next season. Jackson envisions Ledo being able to play some backup small forward in a pinch. Ledo played 12 games down the stretch after being waived by Dallas and showed he can shoot from outside and drive to the hole. He wasn’t in the best shape, needs to improve defensively and take better care of the basketball. He has been working out with Knicks coaches for most of the last 2½ months.

Jackson wanted to re-sign center Jason Smith, but he is expected to have offers greater than what’s left for the Knicks to give him — a starting wage of $2.8 million. It’s too bad because Smith told brass he wanted to come back, believing the system fit him perfectly because of his mid-range jumper.

Also from last season’s roster, defensive forward Lance Thomas and gritty center Lou Amundson have interest in returning, but only the veteran’s minimum is available. Last March general manager Steve Mills said he would like to have both high-character guys back in the locker room.