According to the report, the two sides met in Los Angeles last week in attempts to hammer out a deal, and the team has already offered Aldridge a three-year extension worth $55.5 million.
Aldridge, 28, is scheduled to become an unrestricted free agent next season, and will be in the last year of a $65 million contract. He is on the books for $15,256,000 next season, but the team hopes to sign him to a deal worth $108 million over five years.
Aldridge averaged a career-high 23.2 points and 11.1 rebounds last season for the Trail Blazers, who finished with a 54-28 record and advanced to the Western Conference semifinals.
More from Yahoo Sports:
Aldridge has publicly and privately expressed a strong desire to stay with the Blazers, and there's believed to be significant momentum toward him ultimately recommitting to Portland. The fact that the owner and GM made the trip to present the offer face-to-face wasn't lost on Aldridge's camp, sources said.