Eight Leicester fans have already been detained for public disorder following instances of anti-social behaviour in Madrid's Plaza Mayor late on Tuesday night.
More clashes have occurred in the hours before Wednesday's evening kick-off, with supporters filmed chanting: “F*** off you Spaniards, Gibraltar is ours.”
The chants come amid a heightened state of political tension between the United Kingdom and Spain over the disputed status of Gibraltar, which was ceded to Britain in 1713.
The headland's future as a British Overseas Territory is in the balance ahead of the UK's forthcoming Brexit negotiations with the European Union.
The British government is likely to face the choice of either reaching an agreement with their Spanish counterparts over Gibraltar's status or leaving the territory outside of any prospective trade deal between the post-Brexit UK and the EU.
According to local authorities, the Leicester supporters arrested on Tuesday caused problems into the night and disrespected police officers.
About 100 Leicester fans were in the plaza at the time. Authorities said the disorder began when police officers tried to disperse the crowd.
Spanish media said two officers and three fans sustained minor injuries in the initial confrontations.
The first leg of the quarterfinals will be played at Vicente Calderon Stadium. About 3,000 Leicester fans were expected to make the trip to Madrid to support their team.
Additional reporting by AP