Hoy is tied with Jason Kenny on six golds, and believes Scotland's Archibald could be on course to win half that amount in Japan.
She currently holds one gold medal following her win in the women's team pursuit in Rio three years ago.
Hoy said of the 25-year-old cyclist: “In Tokyo, Katie, depending on who gets selected for what event, could have a great shout at winning three gold medals.
“If she gets selected for three events, she could potentially win three gold medals. That would be absolutely massive.”
Britain's classy Kenny and Archibald win Madison title at London Track World Cup
Hoy believes that Archibald could compete in the team pursuit again, with spots up for grabs in the madison and omnium as well. She holds the 2017 omnium world title, and the 2018 world gold. Laura Kenny is a potential teammate for the madison.
“[If] it’s Laura Katie races with in the madison, they’re the two strongest endurance riders in the world,” Hoy said.
“If Katie gets the nod for the omnium, she could do well in that and in the team pursuit, they have all of the right pieces of the jigsaw, they just need to put it together on the day. So I have complete confidence that they will do very well in the team pursuit.”
Britain's Chris Hoy celebrates after their track cycling men's team sprint finals at the Velodrome (Reuters)
Image credit: Reuters
Hoy explained the pressure an athlete can feel when arriving to defend an Olympic title.
“You suddenly have a target on your back when you’re defending Olympic champion,” he told the Scotland Herald.
“The British girls are used to that though – you can see in the bunch races that every time they go on the attack and they make a move, everyone else responds to it and covers it and that’s one of the biggest challenges, is being the favourite. So in many ways, not winning every race, not winning every major championships between now and the Olympics isn’t a bad thing.
“I think Katie is so used to winning and she wants to win every race she does – it doesn’t matter whether it’s a track league or an Olympic Games so when she doesn’t win, she’s quite hard on herself.”