Sen. Lamar Alexander (R-TN) speaks to reporters before going into the Senate Chamber to vote, on October 12, 2013 in Washington, DC.
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(CNN) —  

Republican Sen. Lamar Alexander announced Monday that he will not seek another term.

“I will not be a candidate for re-election to the United States Senate in 2020. The people of Tennessee have been very generous, electing me to serve more combined years as Governor and Senator than anyone else from our state,” Alexander said in a statement.

“I am deeply grateful, but now it is time for someone else to have that privilege,” he added.

Alexander has represented Tennessee in the Senate since 2003. A source familiar with the matter told CNN that President Donald Trump had called Alexander on Sunday to urge him to run again.

The retirement sets up a wide-open Republican primary in a state where the GOP is dominant.

One potential candidate is outgoing GOP Gov. Bill Haslam. He passed on a run for Bob Corker’s Senate seat in 2018 but built a national network as chairman of the Republican Governors Association and is weeks from leaving office. One Tennessee Republican said a Haslam run would prevent at least some other potential candidates from entering the race.

The state’s GOP members of Congress will also be closely watched. A Trump-style candidate, potentially like Rep.-elect Mark Green, could emerge. The Tennessee Republican, speaking on the condition of anonymity to discuss the potential field frankly, also pointed to Rep. Chuck Fleischmann, former Rep. Stephen Fincher (who lost the 2018 Senate primary to Sen.-elect Marsha Blackburn), US Ambassador to Japan Bill Hagerty and orthopedic surgeon Manny Sethi, who co-edited a health policy book with former Sen. Bill Frist.

Rep. Diane Black, who lost the 2018 GOP gubernatorial primary, finishing third behind Gov.-elect Bill Lee and businessman Randy Boyd, is also the subject of speculation about a potential Senate run.

The race is also sure to stoke speculation about celebrities, including country music stars who are politically active and call Nashville home, as well as sports icons such as former University of Tennessee quarterback Peyton Manning.

CNN’s Manu Raju contributed to this report.