Maynor is making $2.3 million this season and becomes a restricted free agent this summer. The Blazers acquired him in exchange for the draft rights to Georgios Printezis.
Maynor, in his fourth NBA season, is averaging 2.8 points, two rebounds and 10.6 minutes in 37 games with the Thunder this season. He missed most of last season with a knee injury and then got bypassed in the rotation by second-year guard Reggie Jackson earlier this season.
The Blazers acquired the draft rights to Printezis last July in a trade that sent Raymond Felton and Kurt Thomas to the New York Knicks. Portland used the trade exception from that deal to acquire Maynor.
Portland general manager Neil Olshey, speaking at the Blazers' practice facility after the deadline had passed, said he believes Maynor brings the ability to run Portland's second unit while being able to play with the starters.
"He plays with good pace, good tempo, he takes care of the basketball, he makes good decisions and we also think we can experiment a little bit with he and Damian on the floor at the same time," Olshey said.
He also said he is unconcerned about Maynor's knee.
"His playing time right now is in no way related to his knee injury, it's related to the fact that they've got an All-Star point guard and the guy behind him, like I said, was probably one of the premier point guards in the draft, they took Reggie Jackson," Olshey said.
As a result of the deal for Maynor, the Blazers waived backup guard Ronnie Price, who averaged 2.7 points, 1.1 rebounds, 1.9 assists and 13.1 minutes in 39 games. The trade came together about 30 minutes before Thursday's trade deadline, Olshey said.
Lillard said he appreciates the experience that Maynor brings, citing his playoff experience.
"He's seen it all; he will be able to teach me a lot," said Lillard, the NBA's three-time reigning rookie of the month.
Many expected the Blazers to move big man J.J. Hickson, who signed a one-year deal worth a reported $4 million prior to this season. Because he has Bird rights, Hickson had approval of any trade. He would have given up those rights if he agreed to any deal, which could impact the salary he could command in free agency.
"I'm just here controlling what I can control, playing the game of basketball. Off the court, things will take care of themselves like they always have in the past," he said as the trade deadline loomed.
Hickson, in his fifth NBA season, is averaging 12.9 points and 10.4 rebounds per game. He has 28 double-doubles, matching his career high. And he's shot 50 per cent or better from the floor for the last 17 games, a franchise record.
Olshey would not comment about potential deals that never materialized.
"The players that are here, the 14 guys that remain, are all here for a reason," he said. "Suffice it to say, we're not going to comment on any trade speculation about who may or may not have been involved in trade talks over the last couple of weeks. But this is the Portland Trail Blazer roster for the foreseeable future."
Meanwhile, the Blazers (25-29) are mired in a six-game losing streak but are still hoping for a playoff spot. They visit the Lakers on Friday night.