The offer sheet is worth $6.4 million and includes $4 million in year one, NFL.com reported.
Gillislee, 26, led the NFL with 5.7 yards per carry last season. He had 577 yards and eight touchdowns on 101 carries for the Buffalo Bills. He also had a receiving touchdown. Gillislee was a fifth-round pick by the Miami Dolphins in the 2013 NFL Draft.
In March, the Bills assigned an original round tender to the running back worth $1.7 million. The team has five days to match the Patriots' offer. If it doesn't match the offer, it will receiver a fifth-round pick from New England as compensation. A source told the Boston Herald that they don't believe the Bills will match the offer.
The Patriots have Dion Lewis, James White, Rex Burkhead, Brandon Bolden, D.J. Foster, and now maybe Gillislee in a very bunched backfield. New England has yet to re-sign 2016 rushing touchdowns leader LeGarrette Blount, despite their reportedly being an offer on the table for the free agent.