Jairus Byrd wants to discover his true value on the NFL’s open market, and the Buffalo Bills failed to talk him out of it.

The Bills were unable to reach a contract agreement with Byrd by Monday’s deadline to impose the franchise tag, and the team opted not to put the tag on its three-time Pro Bowl free safety.

As a result, Byrd is due to hit unrestricted free agency on March 11, and the overwhelming likelihood is the Bills will lose one of their best players.

“We place a value on a person or player, they have a value they have in their mind, and we just have not been able to meet,” said Bills general manager Doug Whaley, referring to finding agreement on a deal with Byrd and his agent, Eugene Parker.

Whaley kept the door open to reaching a last-ditch deal with Byrd in the next week. However, the odds of that happening are virtually nil.

The franchise tag would have guaranteed Byrd a salary of $8.4 million this year. Had they placed it on him and prevented him from hitting the open market, Byrd surely would have held out until the start of the regular season, as he did last season. Byrd wound up playing 10 complete games for the Bills. But not having the leader of the defensive secondary for all of training camp and preseason – and probably not for 16 games – was a hindrance the Bills didn’t want to repeat, especially at such a high cost.

Buffalo could have tried to tag him and then trade him. But finding a team that would be willing to both pay Byrd a top salary and also give Bills a draft pick would have been difficult.

“That takes another team to do it with,” Whaley said. “So we felt the best thing for the long-term future of the Buffalo Bills was not to tag him. … There’s a lot of moving parts in that situation.”

The Bills also opted not to hit Byrd with a transition tag, which would have allowed them the right to match any offer he received. But it would have guaranteed him almost the same salary as the franchise tag ($8.3 million). What was the point? The Bills obviously already had made their best offer, which was rejected.

“We are very comfortable with the significant offer we made to those guys,” Whaley said.

Exactly how much the Bills offered was not certain. Pittsburgh’s Troy Polamalu tops the safety pay scale at an average of $9.8 million a year. Kansas City’s Eric Berry is No. 2 at $8.34 million a year.

However, the safety market seems bound for inflation. All-Pro Earl Thomas of Seattle and Berry both are entering the last year of their contracts.

Byrd, 27, is a playmaker with great range. His 22 interceptions are the second most of any NFL player over the last five seasons. He’s also a high-character teammate.

Losing Byrd would leave third-year man Aaron Williams as the incumbent free safety. He’s coming off a good year. Whaley said he considers Williams capable of being a No. 1 safety.

How important does Whaley view the safety position?

“It’s an important part,” Whaley said. “Would it be the top-rated piece I would start a defense? No. But it’s in the mix. I think you’d have to start with a defensive end and a corner before you go safety.”

Whaley stressed the Bills have succeeded in keeping some of their own veterans, mentioning Eric Wood and Kraig Urbik, among others.

“I know the fans are going to say why didn’t we get something for him?” Whaley said. “This system is not set up where you can sign everybody. We’ve done a great job signing guys that we’ve had. Look at Leodis McKelvin and Wood last year. Freddie Jackson, Urbik. So we do put an emphasis on signing and keeping our players. It’s just with the salary cap system and the way the NFL is, you can’t keep everybody.”

“But it also makes it exciting for our fans, because they’re excited about Mario Williams. Houston, they lost him for nothing. So that’s just the system we have to deal with. I have complete confidence, not only in everybody in this organization that has given us the resources and the backing, but also in our scouting staff. If we are unfortunate enough to lose Jairus Byrd, we found him. We’ll be confident that we can get a replacement.”

Meanwhile, Whaley said the Bills intend to tender all their exclusive-rights free agents, players with fewer than three years’ experience. They include fullback Frank Summers, receiver Chris Hogan and offensive lineman Antoine McClain. The Bills released linebacker Willie Jefferson, who had signed a contract in January.