Last week, the Chiefs granted the Dolphins permission to talk to Albert, who lives in Miami, about a contract.
If the Dolphins can work out a contract with Albert, it is expected they would give up one of their two second-round picks to make the trade.
Even though he signed his franchise tender, worth $9.82 million for 2013, Albert has skipped the Chiefs' voluntary offseason program. Albert has said he wants a long-term deal and isn't willing to move to the right side of the Chiefs' offensive line.
"I want that long-term commitment," Albert told the NFL Network earlier this month. "But as you know in football, you don't have too much control of the situation. I want to play for the Chiefs, but I want that commitment long term."