Azinger, who captained the US Ryder Cup team to victory on home soil at Valhalla in 2008, made his comments be known during the broadcast of the final day of the 2023 Ryder Cup where Zach Johnson's Team USA were defeated 16.5-11.5 by Luke Donald's Team Europe.
Time for change, you would think?!
Woods, who will be 49 when the 2025 Ryder Cup swings around, was not in attendance at Marco Simone in Rome, Italy, as he continues to recover from ankle surgery.
But the 15-time major champion could be in a position to captain the team in two years' time should he so wish.
That has to be a good sign of Woods' progress as he looks to return to PGA Tour action in the future.
But with his golf career seemingly coming to an end, you would think Ryder Cup captaincy would be a goal very soon.
Woods has had plenty of experience in the captaincy role, too.
Will Tiger Woods captain the 2025 US Ryder Cup team?
Woods then went on to be a playing captain of the 2019 US Presidents Cup team that took care of Ernie Els' Internationals team 16-14 over at Royal Melbourne in Australia.
Another nice tick in the box of Woods is that he won the 2002 US Open at Bethpage Black.
Woods finished the week at 3-under par and three strokes clear of Phil Mickelson.
Despite his incredible PGA Tour career, Woods has only won the Ryder Cup once in eight appearances as a player.
That came at Brookline in 1999.
Woods' record as a US Ryder Cup player stands at: 13–21–3 (W-L-H).
That is a 35% winning record.
Should Tiger Woods become the 2025 United States #RyderCup captain at Bethpage?— GolfMagic (@GolfMagic) October 2, 2023
Will Zach Johnson return to captain the 2025 US Ryder Cup team?
Johnson was heavily criticised for his leadership by a large number of American golf fans this week.
Captain Johnson admitted his team were suffering from head colds and congestion, which was a reason for their lethargic start to the Ryder Cup.
Team USA lost the first two sessions 6.5-1.5 on Friday and it marked the first time ever in Ryder Cup history they had failed to register a single full point on the opening day's play.
After the Ryder Cup concluded, he made a shock admission to the media.
It would therefore seem logical Johnson will not be given another chance when the biennial dust-up swings around in New York in two years' time.
But who knows, maybe he will be afforded another bite at the cherry by the PGA of America.
Another player you would anticipate as a leading contender for the 2025 US Ryder Cup captaincy is Stewart Cink, who acted as one of Johnson's vice-captains in Rome.
Saying that, Cink did come up with one of the most bizarre quotes of all time ahead of the 2023 Ryder Cup.
Who could captain the 2025 European Ryder Cup team?
Azinger considers record European Ryder Cup points scorer Sergio Garcia, who now plays on LIV Golf, could be given a chance to skipper the 2025 European Ryder Cup team should it become possible at the DP World Tour.
Garcia terminated his DP World Tour card earlier this season as a result of the divide in professional golf along with a number of former European Ryder Cup stars also now on LIV Golf such as Ian Poulter and Lee Westwood.
Paul Azinger wonders if the 2025 Ryder Cup at Bethpage Black could feature Tiger Woods vs. Sergio Garcia as captains.— Jeff Eisenband (@JeffEisenband) October 1, 2023
But a Garcia captaincy, at least in 2025, would seem unlikely given Donald is a clear favourite to once again assume the role at Bethpage Black.
Rory McIlroy also wants Donald back, too.
"Two more years, two more years" the players chanted during the victory celebrations at Marco Simone.
Speaking to the media after Europe won the Ryder Cup, McIlroy said he would be "very happy" for Donald to remain in charge.
Eight of the last nine Ryder Cups have been won by the home team.
The last time an away team won the Ryder Cup during that period was Europe at the 'Miracle at Medinah' in 2012.
Should Tiger Woods be given the reigns on the 2025 US Ryder Cup team? What about Luke Donald returning to captain the European team? Should Sergio Garcia be let back into the fray? Share your thoughts and comments on the GolfMagic social media channels.