The Chiefs have settled on Joeckel at No. 1 overall in next week's NFL Draft, a source told CBS Sports.
The report said the Chiefs considered Central Michigan offensive tackle Eric Fisher, but decided Joeckel was a safer pick.
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The Miami Dolphins have received permission from the Kansas City Chiefs to talk contract with offensive left tackle Branden Albert in order to facilitate a trade for a second-round draft choice, a source told ESPN.com.
Albert, who lives in Miami, is expected to visit the Dolphins' facility for a physical in the coming days. His agent, Ron Slavin, can speak only to the Chiefs about a potential deal.
Albert signed his $9.82 million franchise tender for 2013, but skipped the team's voluntary offseason program. The Dolphins will deal one of their two second-round picks to complete a trade.
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The Pittsburgh Steelers have signed restricted free agent nose tackle Steve McLendon to a three-year contract.
Terms of the deal weren't disclosed, but NFL.com reported that it could be worth as much as $7.5 million. Steelers long-time nose tackle Casey Hampton is an unrestricted free agent who is not expected to return.