The Mariners' assistant manager saw his side book a fifth-round meeting with Ruud Gullit and Co after they shrugged aside their dressing-room problems to trounce West Ham 3-0 on Wednesday.
"Ruud who?" quipped the former Stamford Bridge stalwart, who played over 100 games for Chelsea in the Seventies. "We will give them a real fish and chips welcome at Grimsby.
"When you have been in the game a long time you are going to come up against old foes and friends now and again.
"It's nice for me personally that Chelsea will be coming here, but more importantly it is great for Grimsby to have another game against Premiership opponents to look forward to.
"It's good that the people of Grimsby will have the chance of seeing players like Gullit in action."
But Swain knows that Glenn Hoddle's team will provide a bigger challenge than West Ham.
"Chelsea are playing as well as anybody at the moment. They would be a test for any Premiership team, let alone Grimsby.
"The longer you go on in the Cup as a smaller club the more exciting it becomes, but as professionals, our bread and butter has to be getting three points against Reading on Saturday.
"It is another big game for us, but totally different to West Ham. We will have to beware of an 'After the Lord Mayor's Show' display and make sure the players are mentally prepared."
The First Division side, whose only wins since the end of November have been the Cup victories over Luton and now West Ham, will be without their Italian attacker, Ivano Bonetti, for the visit of Chelsea.
Bonetti will not return until next month at the earliest after sustaining a fractured jaw in a row with his player-manager, Brian Laws, after the 3-2 League defeat at Luton on Saturday.
The club hope Laws' apology and the handshake between the two before yesterday's game, which gave Grimsby a huge lift, is the end of the matter, with Bonetti confirming he will stay until the end of the season.
West Ham, whose shock exit came after they had won three Premiership games on the trot, are now left with their regular fight to retain their status in the top flight.
"It was a very disappointing performance from us especially after we had won at Tottenham on Monday," defender Julian Dicks said. "We have got to make sure we lift ourselves for the League."
n David Platt could return for Arsenal against his former club Aston Villa next week after a successful comeback match yesterday. Platt, who has been out for a month after undergoing a second knee operation, came through 90 minutes in a specially arranged friendly against Coventry.