One source told Schefter he doubts a deal gets done.
The two sides had been discussing a potential trade that would give the Chiefs a second-round pick, but shelved the talks while the first round of the draft was underway Thursday night.
Chiefs general manager John Dorsey said he spoke with Dolphins GM Jeff Ireland midway through the first round and they agreed to speak again Friday, before the second and third rounds.
"We'll see what happens," Dorsey said Thursday. "That's kind of where we're at."
The Dolphins, who have been in the market for a left tackle, appeared as if they were moving into position to select Oklahoma's Lane Johnson when they traded into the Oakland Raiders' pick at No. 3, but instead went with Oregon defensive end Dion Jordan.
The Chiefs negotiated with Albert on a long-term deal this offseason, but the two sides were never close to an agreement. So the Chiefs placed the franchise tag on Albert in March, and he signed a tender that would pay him about $9.3 million next season.
But Albert has repeatedly said he's unhappy without long-term stability, and that he's unwilling to play anywhere other than left tackle.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.