Around 1,500 Linfield supporters are expected to travel from Belfast to see their club play in Glasgow in a Champions League qualifier on Wednesday.
Officers said there will be a “robust” policing plan in place and they have advised people to comply with all safety and security arrangements at Celtic Park.
Celtic had refused their ticket allocation for the first leg of the second qualifying round match in Belfast on Friday due to security fears.
However, there were around 300 Hoops fans in the Kop stand, set aside for them in a half-full stadium, to see goals from Scott Sinclair and Tom Rogic give the Scottish champions a 2-0 lead for the return match at Celtic Park.
The game was hit by trouble, however, when Celtic striker Leigh Griffiths had a bottle thrown at him as he prepared to take a corner kick.
Speaking ahead of Wednesday’s match, Police Scotland’s event commander Superintendent Craig Smith said: “Glasgow once again is in the spotlight as Celtic host Linfield on their return leg.
“As would be expected at such an event, there will be a robust policing plan in place with public safety being paramount.
“We’ve been working with a range of partners including the Police Service of Northern Ireland in our planning in the lead up to the match.
“There will be additional officers in and around Glasgow to assist those supporters attending the match. We’ll also have officers at transport hubs to ensure fans get there safely, working with British Transport Police officers.
“Although the majority of supporters attending these matches are well-behaved and enjoy the game, there is often a minority who are intent in drinking too much alcohol and engage in criminal behaviour such as disorder, offensive behaviour and vandalism.
“Plan your outing in advance, know your travel plans, drink responsibly and be aware of restrictions on what you can bring into the stadium. Anyone who is intent in causing disorder or hate crime can expect to be arrested by police.
“Let’s keep this match focused on the football.”
Police reminded fans it is an offence to use threatening, abusive or insulting words or behaviour or to display written material likely to stir up hate crimes, and to enter the sports ground with any pyrotechnic device.
Other offences include being drunk in a sports stadium or aboard a coach or minibus taking people to a sporting event.