The League One outfit came through a first-round tie with Torquay United, before being rewarded for an impressive 2-0 success away at Queens Park Rangers with a third-round home draw against Chelsea.
And Cooper, who replaced Kevin MacDonald in charge at the County Ground last month, is relishing the chance for his side to take on such high-quality opposition.
"It's another fantastic test for the players," the 44-year-old said.
"It’s great for the club, I'm sure it will be a full house. It will be all about the players and the club and the fans.
"We'll prepare the best we can but we'll have to prepare to play against some of the best players in the world."
Swindon - who won the League Cup in 1969 as a Third Division side, beating Arsenal 3-1 in extra time - have had a mixed start to their League One campaign.
Cooper’s side have taken 11 points from their eight games so far, and occupy 11th place after their 3-2 win over Bristol City on Saturday.
Meanwhile, their Premier League opponents have had a similarly indifferent start to their own campaign, despite Mourinho’s much-heralded return to Stamford Bridge.
After consecutive home wins over Hull City and Aston Villa, Chelsea went four games without a win in all competitions - drawing with Manchester United before losing to Bayern Munich on penalties in UEFA Super Cup, Everton in the Premier League and Basel in the UEFA Champions League.
However, Mourinho's men bounced back at Stamford Bridge on Saturday with a 2-0 win over Fulham, thanks to goals from Oscar and John Obi Mikel.
Mourinho twice led Chelsea to League Cup glory in three years during his first spell in charge, beating Liverpool and Arsenal in the 2005 and 2007 finals to claim the club’s third and fourth triumphs overall.
His successor Avram Grant also took the side to the final in 2008, but they were beaten 2-1 by Tottenham in extra time.
Chelsea will be hoping for a repeat of the last time they met Swindon, when goals from Gavin Peacock and Dennis Wise handed them a 2-0 win in the Premier League in 1994.
But Swindon were victorious in the only previous League Cup meeting between the two, running out 3-0 winners back in 1963.
Juan Mata will start for Chelsea on Tuesday, Mourinho has confirmed, after the Spaniard was missing from the squad on Saturday.
Mourinho has also revealed that David Luiz, Michael Essien, Ryan Bertrand and Cesar Azpilicueta will all feature.
