NBA.com first reported Thursday that Portland was expected to sign Kanter to the offer sheet.
A league source told ESPN's Ramona Shelburne that the Oklahoma City Thunder are determined to match the offer sheet. They now have three days to do so.
After being acquired by the Thunder at the trade deadline from the Utah Jazz in a three-team deal, Kanter became an interior force for Oklahoma City, particularly because of his immediate pick-and-roll chemistry with point guard Russell Westbrook.
Before Kanter arrived, no Thunder center in the Oklahoma City era ever had recorded a 20-point, 10-rebound game. In 26 games with the Thunder, Kanter had 11.
Thunder general manager Sam Presti had been very direct in saying he wanted to re-sign Kanter.
"We wouldn't have traded for him if we didn't feel like we're going to be in a position to have him with us going forward," Presti said in April.
Kanter, a 6-foot-11 Turkish center, compiled 17 double-doubles with OKC, averaging 18.7 points and 11.0 rebounds per game. He played only 10 games with Serge Ibaka and none with Kevin Durant, however, because of injuries.
Kanter was selected third overall by the Jazz in 2011, but he never found much footing in Utah, getting caught in a frontcourt logjam. It led to Kanter requesting a trade in January and then making strong, negative comments about his time with the Jazz.
Kanter, 23, holds career averages of 10.2 points and 6.4 rebounds per game in three seasons.
Also Thursday, the Blazers and point guard Damian Lillard completed the five-year contract extension worth more than $120 million they agreed to last week.
The extension keeps Lillard under contract through the 2020-21 season and makes him the unquestioned franchise pillar after LaMarcus Aldridge, Wesley Matthews and Robin Lopez left in free agency and the team traded Nicolas Batum to Charlotte.
Aminu agreed to a $30 million, four-year contract last week; Davis agreed to a $20 million, three-year deal.
ESPN.com's Royce Young and The Associated Press contributed to this report.