Bills chief operating office Russ Brandon and football administration chief Jim Overdorf met here with Greer's agent, Mark Bloom, on Saturday and are expected this week to make another proposal, an NFL source informed me.
Greer can become an unrestricted free agent on Friday.
On Saturday, I wrote how the sides were laughably far apart on financial terms and that it appeared Greer was going up for bids.
"I'm excited about the opportunity of my life," Greer said. "I'm in position to have the opportunity to evaluate what I'm worth. It'll be fun. I'm interested to see what other teams are going to do."
Now the Bills want to give Greer at least something to think about before he hits the open market.
Greer, undrafted out of Tennessee, has played five NFL seasons. He missed six games with a knee injury last year, but started all 10 of the other games at right corner. Greer recorded 43 tackles and two interceptions, returning both for touchdowns. He defensed nine passes and forced a fumble.