The Dolphins called on more than one occasion over the past few weeks but were told by the Bengals that they are not trading the pick and will stay at No. 1, sources said.
Miami has an NFL-high three first-round picks -- Nos. 5, 18 and 26 -- and has been widely speculated as a possible candidate to trade up in the round. The Dolphins also have a league-high 14 total selections in this draft.
The Dolphins have shown interest in a number of potential first-round quarterbacks, including Alabama's Tua Tagovailoa and Oregon's Justin Herbert. Last week, Dolphins general manager Chris Grier said he has gotten to know Tagovailoa and Herbert through the draft process, calling them both "interesting kids."
ESPN's Mel Kiper Jr. predicted that Miami would select Tagovailoa at No. 5, defensive tackle Javon Kinlaw at No. 18 and offensive tackle Josh Jones at No. 26 in Kiper's most recent mock draft, released Thursday morning.
The Bengals are expected to draft LSU quarterback Joe Burrow with the first pick Thursday. Sources told ESPN's Dianna Russini on Wednesday that the Bengals want to wait until they are on the clock to make it official, giving Burrow that special moment when he gets the call from his new team.
Bengals coach Zac Taylor told ESPN's Get Up on Wednesday that he has enjoyed getting to know Burrow, but he wouldn't confirm what Cincinnati would do with the pick that kicks off this year's draft.