Four years ago, ahead of London 2012, Muhammad was controversially selected ahead of Cook, who was regarded as the world number one at the time, but still went on to claim the bronze medal in the under 80kg category.
As a result of the "snub", Cook switched allegiance to Moldova, meaning the pair could meet in the final at the Carioca Arena 3 on August 19 if both make it that far through the competition.
"We are not friends," Muhammad said of his relationship with Cook.
"There's always fireworks when we fight, it's always exciting, it's the fight the crowd wants to see.
"It's probably the biggest rivalry in taekwondo.
"I embrace it.
"Cook is a world-class athlete, he's always going to be dangerous.
"Do I think I'm better than him? Absolutely.
"The place to prove that is in the ring.
"I've got four fights to win an Olympic gold medal.
"If he is one of those fights, I welcome it."
In their four previous fights, the two cannot be separated with both competitors winning two each.
"That makes it even more tasty for a fifth fight," Muhammad added, before revealing he has no problems with team-mate Walkden.
"Bianca's great about it," he said.
"She's been going out with him for years.
"She's good at keeping her personal and professional life separate.
"I've never had a problem with Bianca."
Muhammad, nicknamed the Walthamstow Warrior after the London borough in which he was born, received hate mail when selected ahead of Cook.
“It was very tough on my family," he said.
“But they did a wonderful job of shielding me from a lot of the silly stuff, so did GB Taekwondo.
"They kept as much of it away from me as they could.
“It was terrific getting a medal in my home town, in front of my home fans.
"It proved a point.
"But it made me more hungry to win a gold medal."