Brown, who sported No. 1 at Ole Miss, has worn No. 11 since his rookie season after initially donning No. 18 during rookie minicamp.
Jones, who rocked No. 8 at Alabama, also wore No. 11 for his entire Atlanta Falcons career, but he rejected the jersey number when Brown offered it to him.
"#11 until I retire. I tried to give it up and he wouldn't take it. Respect," Brown wrote on Twitter.
Later Tuesday, the Titans announced that Jones will wear No. 2 in the 2021 season.
The Falcons traded Jones to the Titans on Sunday in exchange for a 2022 second-round draft pick and a 2023 fourth-rounder. Atlanta also sent a 2023 sixth-round selection to the Titans in the deal.
Earlier Tuesday, Jones -- who spent his first 10 NFL seasons with the Falcons -- made his first public comments since being traded. In a statement posted to social media, the All-Pro receiver said he'll "never forget my time as an Atlanta Falcon."
"Thank you ATL for all the love you've shown me over the years," Jones said. "It's been an amazing 10 years playing for the city and all the fans. I appreciate everything you've done for me over the years and will never forget my time as an Atlanta Falcon.
"Excited for the next part of my journey here in Nashville. To the fans, I want to thank you all for the warm welcome for me and my family. We are very excited to be part of the Titans family. Ready to get to work!"
The Falcons selected Jones with the No. 6 overall pick in the 2011 NFL Draft out of Alabama. He finished as the franchise's career leader in receptions (848) and receiving yards (12,896) and is second to Roddy White in touchdown catches (63).