The offer was confirmed Thursday by a person close to the negotiations who could not comment publicly because the team had not formally announced it. The offer, made to Aldridge's representatives last week, was first reported by Yahoo! Sports.
Aldridge, in the fifth and final year of a $65 million contract, is set to become a free agent next summer. The Blazers hope to lure him to stay with a five-year, $108 million extension.
Aldridge averaged a career-best 23.2 points and 11.1 rebounds last season for the Blazers, who went 54-28 and advanced to the Western Conference semifinals before losing to eventual NBA champion San Antonio.
The move does not come as a surprise after general manager Neil Olshey emphasized the importance of getting the deal with Aldridge done.
''The most important thing is everybody, including LaMarcus, knows he's the number one priority in the organization right now,'' Olshey said when the season ended.
There was talk last summer that Aldridge was interested in entertaining other offers, but as the season drew to a close he said several times that he was happy in Portland.
The Blazers have been known in recent years to pull off draft night surprises, but the team was quiet with no picks this season.
It was the third time that the Blazers had gone without a selection, but first since 1999.
The team surrendered its picks in this year's draft because of earlier trades. The No. 24 overall pick went to the Charlotte Hornets as part of a 2011 trade that brought Gerald Wallace to Portland. The No. 56 pick went to the Denver Nuggets in the 2011 trade that sent Andre Miller to the Nuggets.