The Crabbe offer sheet was first reported by The Vertical and confirmed by ESPN.
The contract could reach up to $83 million in bonuses and includes a player option for the fourth season, sources told ESPN.
The Trail Blazers have three days to match the offer.
This is the second restricted free-agent offer sheet Brooklyn general manager Sean Marks has given out. Miami Heat restricted-free-agent guard Tyler Johnson signed a four-year, $50 million offer sheet with Brooklyn, which contains a poison-pill provision.
Marks has been aggressive in rebuilding the Nets, also signing Jeremy Lin (three years, $36 million) and agreeing with Trevor Booker (two years, $18 million) and Justin Hamilton (two years, $6 million).
Crabbe, 24, emerged as a quality scoring threat off Portland's bench last season, when he averaged 10.3 points in 26 minutes per game and shot 45.9 percent from the floor and 39.4 percent from 3-point range.
The 31st overall pick in the 2013 draft, Crabbe seized an opportunity for a significantly increased role in 2015-16 due to the Trail Blazers' youth movement. He played in only 15 games as a rookie and averaged only 3.3 points in 13.4 minutes per game in his second season.
Information from ESPN.com's Tim MacMahon was used in this report.