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BUFFALO (CBSMiami/AP) — If the Miami Dolphins are going to hang on to tight end Charles Clay, it’s going to cost them more than they hoped it would.

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Clay moved one step closer to leaving the Dolphins after signing the Buffalo Bills’ five-year, $38 million contract offer on Tuesday night.

A person familiar with the situation told The Associated Press that the Bills extended Clay the offer. And a second person told the AP that Clay had signed it. Both people spoke on the condition of anonymity because the Bills and Clay have not publicly discussed their negotiations.

The signing means the Dolphins have five days to match the offer or lose Clay to Buffalo without compensation. Miami retained the right to match after awarding Clay a transition tag two weeks ago. The move ensured that Clay will make at least $7 million this season.

The Dolphins could be handcuffed by salary-cap constraints to match the Bills’ offer after Miami signed free-agent All-Pro defensive tackle Ndamukong Suh to a $114 million, six-year contract last week. It made Suh the highest-paid defensive player in NFL history.

The Bills made Clay one of their top free-agent targets this offseason. Clay traveled to Buffalo by private jet on March 10, the first day of the league’s signing period. He then spent several days in town to meet with team officials and tour the region.

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Clay has been a four-year starter in Miami since being selected in the sixth round of the 2011 draft. He had 58 catches last season for 605 yards and three scores. Overall, he has 161 catches for 1,809 yards and 14 touchdowns in 58 games.

At 6-foot-3, and 255 pounds, Clay has the prototypical size and catching ability of a tight end that would fit the run- and short-pass oriented offense the Bills are introducing under new coach Rex Ryan and offensive coordinator Greg Roman.

The Bills have already opened room on their roster to have Clay step in as a starter. Buffalo released Scott Chandler last week, and did not re-sign veteran backup Lee Smith, who has since signed with Oakland.

Their departures left Buffalo with only two tight ends on the roster, Chris Gragg and Marqueis Gray, who appeared in five games last season after the Bills claimed him off waivers.

The Bills, coming off a 9-7 season, have already been busy upgrading an offense that finished 26th in the league last season.

Two weeks ago, Buffalo acquired running back LeSean McCoy in a trade with Philadelphia. On Friday, they agreed to sign free agent receiver Percy Harvin to a one-year contract.

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(TM and © Copyright 2015 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2015 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)