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 going on 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. "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.
"Actually, I had walked out of the room, and you saw that happen," Dorsey said. "Dion Jordan is a very good football player, and he'll help out that defense. We'll see what happens. How can one club figure out what another club is doing in this draft?"
The Dolphins traded away the higher of their two second-round picks, No. 42, in order to move up in the first round. They also have the 54th overall selection, which could be enough to acquire Albert, a former first-round draft pick of the Chiefs.
"Would I make that trade if it was offered to me? I don't know," Dorsey said. "That's an unknown. Until something happens, I really don't know."
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. Those two factors, along with a back injury that kept him out for several games last season, could be enough for the Chiefs to deal him.
"I think Branden Albert is a hell of a football player," said Dorsey, who has maintained that the selection of Fisher had nothing to do with whether Albert stays or goes.
"All along, I've told you, we'll take the best available player," Dorsey said. "At the end of the day, he was the best available player."