The Dolphins and Chiefs have agreed not to further discuss a potential trade involving Kansas City left tackle Branden Albert until after both teams make their first-round selections in Thursday night's NFL draft, according to a league source.

That assumes the Dolphins haven't chosen an offensive tackle with the 12th overall pick -- or haven't succeeded in moving up for one of the tackles the Chiefs ignore with the top selection.

The Chiefs pick first with increasing speculation they prefer Central Michigan's Eric Fisher over Texas A&M's Luke Joeckel.

That would leave Joeckel and Oklahoma's Lane Johnson for the teams with a priority of acquiring a left tackle -- the Detroit Lions, Arizona Cardinals, San Diego Chargers and Baltimore Ravens among them. That could inspire some of those teams to attempt to trade up since Joeckel is believe to be the top-rated player on many draft boards.

If the Dolphins draft a tackle to replace Jake Long, their interest in trading for Albert will vanish, and the Chiefs then might be stuck with a player who carries a $9.8 million franchise tag who plays the same position as the player chosen first overall.

Chiefs general manager John Dorsey previously said the team is not letting Albert's status deter it from taking the best player on its board Thursday night.

"I don't think you can do that," Dorsey said.