The Utah Jazz have seven days to match the offer. The terms were not disclosed by the Blazers because of team policy.
Millsap's agent did not immediately respond to phone calls and e-mails from The Associated Press seeking comment.
Millsap averaged 13.5 points for the Jazz last season, getting double-doubles in 19 straight games while starting for Carlos Boozer, and has career averages of 9.4 points and 6.4 rebounds since the Jazz selected him with the No. 47 pick in the 2006 draft.
The Jazz already have high salaries committed to a number of players for next season, including Boozer. He was expected to opt out of his contract and become a free agent, but declined the option and Utah owes him $12.7 million. Deron Williams, Andrei Kirilenko and Mehmet Okur all will earn at least $9 million, meaning the Jazz could be well over the salary cap if they match the offer to Millsap.
The Trail Blazers were $7.7 million under the salary cap after the league set it at $57.7 million for next season. The cap is determined by a percentage of league revenue from the previous season.
ESPN.com reported Friday night that Portland's offer to Millsap was for four years and up to $36 million.
Should the deal go through, the 6-foot-8 Millsap could back up Blazers forward LaMarcus Aldridge.
Asked whether the team had reservations about spending money on a bench player, general manager Kevin Pritchard said Thursday: "I'm a big believer in that you get the best player."
Last week, the Blazers showed interest in free agent forward Hedo Turkoglu, but talks crumbled.
Turkoglu, who helped Orlando to the NBA finals, was in Portland last week to speak with the Blazers before negotiations were abruptly cut off. He has since been acquired by the Toronto Raptors.
The announcement concerning Millsap capped an eventful Friday for the Trail Blazers.
First came word that draft pick Patty Mills had broken his foot Thursday night during a practice for the NBA's summer league. He was scheduled for surgery on Monday.
