The sudden retirement announcement of veteran Rep. Ander Crenshaw has ignited speculation about a high-profile successor: former University of Florida quarterback Tim Tebow.

The 4th District, now represented by Mr. Crenshaw, 71, includes the Jacksonville area, where Mr. Tebow maintains a residence, a business — sports-consulting firm XV Enterprises — and the Tim Tebow Foundation.

Two weeks ago, Mr. Tebow, 28, said in an interview during his foundation’s annual golf tournament that he found the idea of entering politics “intriguing.”

“I don’t know at this time in my life,” Mr. Tebow said March 29 on “Fox & Friends.” “[I]f there’s a chance you can make a difference someday at something, then that would be intriguing.”