It will be the first time an SPL side played in Manchester since Rangers were beaten in May's UEFA Cup final.
Manchester City Council and Greater Manchester Police are desperate to avoid a repeat of the ugly scenes involving a minority of supporters following the game.
"Manchester is looking forward to welcoming Celtic fans visiting the city for Tuesday October 21's UEFA Champions League tie with Manchester United. We're a city that's passionate about football with a proud reputation for hospitality.
"In return, we are sure that Celtic fans will want to uphold the great reputation of the club and its travelling supporters.
"Along with Celtic, we are urging supporters who do not have tickets not to travel to the city. Ticketless supporters will not be able to get into the game and facilities will not be provided for fans to watch the match elsewhere.
"We promise to show the greatest respect to visiting Celtic fans and are sure that they will respond in kind by helping keep our streets litter-free and abiding by local bye-laws.
"These laws obviously include a ban covering on-street drinking and this will be enforced.
"We have welcomed Celtic supporters to Manchester on many previous occasions with great success. We are sure next week will enjoy the same great experience. We hope you will all enjoy the match and visiting Manchester."
Celtic chief executive Peter Lawwell added: "Celtic supporters have a tremendous reputation and have become renowned across Europe for the positive manner in which they travel and support the club.
"This was again in evidence just a few weeks ago when our supporters travelled to Villarreal in numbers and despite the result once again made friends and enjoyed a great sporting occasion.
"We have met on a number of occasions previously in both competitive and friendly matches, with thousands of our supporters travelling to the city to honour such great footballing names as Bobby Charlton, Mark Hughes, Roy Keane and Ryan Giggs.
"We are sure our fans will travel to Manchester once again with the aim of supporting the club positively as they enjoy another great meeting between two of Europe's great clubs.
"We would like to thank the city of Manchester in advance for hosting our club and our supporters next week."