Ian Maxwell, chief executive of Scottish football’s governing body, has offered up the national stadium to the new undisputed super-lightweight champion of the world.
Hampden last hosted a major boxing contest in June 2000 when Mike Tyson defeated Lou Savarese in 38 seconds.
Taylor is a hot property after his points victory over Jose Ramirez in Los Angeles at the weekend when the 30-year-old became only the fifth man to simultaneously hold all titles since the four-belt era officially began in 2004. He is the first British boxer to do so.
Hearts reach a decision on Jacob Davenport contract
Edinburgh's Tynecastle Stadium: Here are 20 pictures from the 1950s and 1960s showing how much the Hearts ground has changed
Hearts debrief: Barrie McKay's threat, several missed chances, need for another forward
'Not good enough.' Hearts hit out at Hibs fans as lighter hits Alex Cochrane at Easter Road
Hibs hero Martin Boyle: I've never felt anything like Edinburgh derby equaliser against Hearts
The Prestonpans fighter said he would like his next fight to be on home turf and expressed a preference for Edinburgh Castle or Easter Road.
But Maxwell said: “There is no reason why we can’t have a boxing fight at Hampden. I think Mike Tyson was the last one to fight there and it lasted less than a minute. So hopefully Josh can have a fight there and it would last less than a minute and everybody would be happy.”
Speaking to STV, the SFA chief added: “He has a huge profile in the boxing community. He’s a superstar after his performance at the weekend and we would love to have him at the national stadium.”
“I think there would be a huge amount of interest in Josh Taylor given the level he is now at. Being undisputed champion is a fantastic achievement.
“Taylor’s first fight in defence of all of his belts he has at this point at the national stadium is something we would love to see.”
Taylor’s next fight could be against Chorley’s Jack Catterall, who had been the mandatory challenger for the WBO belt that Ramirez put on the line, but bigger fights await, possibly at welterweight (147lbs).
“We will see what comes my way, I am not going to be short of options,” Taylor said after his victory over Ramirez by a unanimous decison. “Every fight is going to be huge. I will just ride the wave.
“I would like to go up to 147 and chase a real, real big fight like Terence Crawford. I am not going to call him out, he is a great fighter, but two undisputed champions going at it at 147 would be awesome.
“There’s big fights at 140. I am not afraid to fight anybody. We might have to fight Catterall first as well, he agreed to step aside to let this fight happen so if we have to do that next, we have to do that next, but if something bigger comes along, we might have to do that.
“I’ve not boxed in my home city for a few years so I would love to take a big fight back to Scotland. Now is the time to get that fight at Edinburgh Castle or Easter Road.
“I know they will have me at Easter Road, they have said it to me a few times, but I’d love to fight at Edinburgh Castle, it would be iconic to have the castle lit up in the background.”