Brees created a social media stir Sunday night when, as part of a tweet to address "speculation" about his future, he said he "may play football again."
Brees, 43, retired from football in March 2021 and spent last season as an NFL analyst for NBC. The 13-time Pro Bowl quarterback tweeted Sunday in apparent response to the New York Post, which reported that Brees will not return to NBC for the 2022 season.
Despite speculation from media about my future this fall, I'm currently undecided. I may work for NBC, I may play football again, I may focus on business and philanthropy, I may train for the pickleball tour, senior golf tour, coach my kids or all of the above. I'll let you know— Drew Brees (@drewbrees) May 15, 2022
Allen, speaking Monday at the Saints' Hall of Fame golf tournament from Kenner, Louisiana, said there have been no discussions about a Brees comeback in New Orleans.
"I think it was a comment made in jest, and we certainly haven't had any conversations in that regard," Allen said.
Brees is second in NFL history in career passing yards (80,358) and touchdown passes (571), trailing only Tom Brady in both categories.
Amid Brady's comeback from a brief retirement this offseason, Allen was asked whether he still thinks Brees can perform at a high level in the NFL.
"I don't really want to live in those hypothetical worlds right now," Allen said. "We'll see where it all goes, but he caused a lot of interest, that's for sure."
Saints general manager Mickey Loomis also said he had not spoken to Brees.
When asked if he thinks Brees would be capable of a comeback, Loomis said Brees is "capable of anything he wants to do" but said he would "stay away" from any speculation about whether the former Super Bowl MVP might actually consider a return.
The Saints went 9-8 but missed the playoffs last season due in part to injuries and inconsistency at quarterback.
Jameis Winston is expected to be New Orleans' starting quarterback in 2022 after signing a two-year extension worth a base value of $28 million this offseason, with veteran Andy Dalton serving as the backup.
ESPN's Mike Triplett contributed to this report.