Regis, who sadly passed away two years ago, is remembered as one of the true greats in the entire history of West Bromwich Albion - who host Leicester City in the Premier League on Sunday.
In the first instalment of a new series on LCFC.com, offering Foxes legends a chance to pick out one illuminating figure from the past for City's 2020/21 opponents, Cottee remembers Regis' pioneering impact on English football.
Born in Maripasoula, French Guiana, his family moved to England in 1962, before quickly impressing scouts across the country with his exceptional performances at semi-professional level for Molesey and Hayes.
It is said that West Brom scout Ronnie Allen initially struggled to persuade the board to part with £5,000 to seal the transfer - so he offered to put up his own money to get the deal over the line.
Ever since netting a brace on his Albion debut in August 1977, Regis became an icon for a whole generation of football fans, scoring more than 200 goals in just under 750 professional appearances.
He won five England caps and also had spells playing for Coventry City - where he lifted the FA Cup in 1987 - as well as Aston Villa, Wolverhampton Wanderers and Wycombe Wanderers.
His Goal of the Season against Norwich in the FA Cup in 1982, meanwhile, was regularly broadcast during the opening titles for Match of the Day - one of Cottee's early footballing memories.
"I remember that goal so, so well," Cottee said. "He turns and dribbles a little bit and then just smashes it from about 30 yards into the top corner! He scored a wonderful goal at Old Trafford, too, I remember.
"He was a big, strong boy. It's funny, really, because when you see people play on the telly, you think that they're massive and you envisage them being about 6ft 4ins.
"When I actually met Cyrille in real life, he wasn't as tall as I was expecting him to be, but he was a really nice man and I enjoyed speaking to him about his incredible career in the game.
"I know we lost him a few years ago, but he was a wonderful player. He was really, really good in the air. As I say, he wasn't massively tall, but he had an incredible spring.
"He was a very athletic type of guy and he was a really, really good finisher. He's someone that, as a smaller player myself, I would have absolutely loved to have played alongside.
"He seemed to be very much a team player - a complete team player. Cyrille could do everything and he just had a really good all-round game."
Over Regis' seven seasons in the West Midlands, he was top scorer four times, as a vibrant Baggies outfit regularly challenged for honours, both in the First Division and the cup competitions.
Later on, Ron Atkinson's men were an exciting side that included Bryan Robson and two other black stars of their eras, Laurie Cunningham and Brendon Batson.
It was still unusual at the time for three top black players to all play for one team and their performances - earning them the nickname 'The Three Degrees' - inspired a generation of black youngsters.
In West Bromwich town centre, meanwhile, a statue depicting the trio - who 'opened the gates for black players' - can be found in tribute to their immeasurable impact on the game.
Representing England in European competitions as well as impressing back at home, Atkinson's West Brom side were one of the most entertaining footballing sides in the country at the time.
Cottee, who is Leicester City's fifth all-time top Premier League goalscorer, remembers that Baggies team well and paid tribute to the 'incredible' talent on show from Regis in particular.
"They had Robson in the midfield, along with players like Remi Moses, Brendon Batson, Laurie Cunningham and, of course, Cyrille," he remembered.
"They had some really, really good players. Tony Brown would have been just coming towards the end of his career too. Atkinson was a very flamboyant manager as well.
"Black players weren't in the game so much, obviously nowhere near as much as what they are now, and they were nicknamed 'The Three Degrees'.
"There was something different about them and the style of football, as well, was just incredible."
Like so many black players at that time, Regis had to endure abuse throughout his career - but Cottee says his supreme talent enabled him to silence anyone in the terraces with malicious intent.
"They were hostile times, let's be honest," Cottee added. "The black players were certainly singled out for a lot more stick than the white players.
"It never used to faze people like Cyrille and there was another guy called Clyde Best, who played at my old club, West Ham.
"He arrived in the early '70s and, you know, you used to go to the game and hear all the abuse that he was getting. They never let it affect them, rile them or worry them.
"They just chose to get on with it and do what they were best at, which was scoring goals. Both Clyde and Cyrille were great goalscorers, and they just got on with their game.
"Above all, I would remember Cyrille as a gentleman because, whenever I met him, he was such a nice guy - a really, really nice man. He was a real pioneer.
"We all have our different pioneers or icons, but I think Cyrille will be remembered as a real trailblazer and someone who set the standard, really, for players in this country."