With former LSU assistant Joe Brady taking over as Carolina's offensive coordinator, there has been mounting speculation that the Panthers are plotting to move up to the No. 1 pick to draft Heisman Trophy winner Joe Burrow.

But any speculation involving Carolina, Miami or any other quarterback-interested team should be quickly dispelled, because the Bengals have no intention of trading away the No. 1 draft pick, league sources familiar with the situation told ESPN.

Cincinnati plans to stay right where it is, according to sources, and presumably fill the biggest need on its roster -- quarterback. The Bengals, in the opinion of many, cannot pass on a potential franchise quarterback in Burrow, whose father already has said his son has no qualms about going to Cincinnati.

The Bengals had the No. 1 overall pick three other times -- 1994, 1995 and 2003 -- and they never have traded out of that slot before. They did move up to No. 1 in 1995.

Burrow, who led LSU to an undefeated season capped by a victory in Monday's College Football Playoff National Championship, has plenty of experience playing football in Ohio. He played high school ball at Athens High School, which is less than 160 miles east of downtown Cincinnati, and then spent three seasons at Ohio State before transferring to LSU for his final two years of college.

Burrow posted some of the best numbers in collegiate history this past season, setting the Football Bowl Subdivision single-season records for passing touchdowns (60) and touchdowns responsible (65). He thrived under the 30-year-old Brady, who spent this past season as LSU's passing-game coordinator before returning to the NFL this past week to join new head coach Matt Rhule at Carolina.

ESPN's Mel Kiper has Burrow ranked as the No. 2 overall prospect in April's draft, and ESPN's Todd McShay projects he will go to Cincinnati with the No. 1 pick.

ESPN's Ben Baby contributed to this report.