The offer is for two years and is worth $6.4 million, including $4 million in the first year, sources told ESPN. The Bills have five days to decide whether to match the offer sheet.
The Bills placed an original-round tender on Gillislee worth $1.797 million, meaning the Patriots would send a fifth-round pick to the Bills if Buffalo declines to match. The Dolphins picked Gillislee in the fifth round of the 2013 draft but released him in 2015.
The financials were first reported by NFL Network.
If the Bills decline to match Gillislee's offer, it is unlikely the Patriots will re-sign free-agent running back LeGarrette Blount, who led the NFL with 18 rushing touchdowns, which was the highest total in the NFL since Adrian Peterson had 18 in 2009. He was the Patriots' top power running back, totaling 1,161 yards on 299 carries in the regular season.
Gillislee set career highs last season with 577 yards receiving and nine touchdowns (eight rushing) in 15 games, including one start. His 5.7 yards per rush average led the NFL.
This is the second consecutive offseason the Patriots have signed a Bills player to an offer sheet. In 2016 they did so with wide receiver Chris Hogan and Buffalo declined to match the offer.
Hogan went on to post a career-best 680 yards receiving with 38 receptions and four touchdowns. He tied for the NFL lead with his 17.9 yards per reception average.
Hogan had 17 receptions for 332 yards in the playoffs and caught two touchdown passes in the Patriots' 36-17 AFC Championship Game victory over the Pittsburgh Steelers.
The Patriots also signed former Bills cornerback Stephon Gilmore at the outset of free agency, poaching another impact player from their division rival.
ESPN's Mike Reiss contributed to this report.