West Yorkshire Police confirmed they had been contacted by The Safer Schools Officer for Corpus Christi Catholic College.
The incident took place on Wednesday afternoon on playing fields across from the school in Halton Moor.
It is alleged that during a schools rugby match - which the YEP understands was played between Corpus Christi and Abbey Grange Church of England Academy - racist comments were made by a group of youths "from the local area who had congregated nearby".
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A crime has now been recorded for a racially aggravated public order offence in relation to the incident.
Police are working with the schools - which have both provided statements confirming the incident to the YEP - and have launched an appeal.
James O'Doherty - Principal of Corpus Christi Catholic College - said the school "do not condone any discriminatory or offensive behaviour".
In a statement provided to the YEP, he said: "We are aware of an incident that occurred off-site by a member of the public unrelated to either school.
"The police have been made aware.
"As a College, we do not condone any discriminatory or offensive behaviour."
A spokesperson for Abbey Grange Church of England Academy said that in "a tough climate", their staff and pupils "responded with great dignity and maturity".
"School is currently offering support to the pupils involved.", the spokesperson added.
Inspector Jodie Scatchard, who heads the Leeds East Neighbourhood Policing Team, said: “The Safer Schools Officer for Corpus Christi Catholic College was made aware yesterday morning of an incident on Wednesday afternoon during a schools rugby match on the playing fields across from the school, where racist comments were made by some of a group of youths from the local area who had congregated nearby.
“A crime has been recorded for a racially-aggravated public order offence and we are working with the schools involved to support them following this incident.”
Anyone with any information that could assist in identifying the suspects is asked to contact officers via 101 quoting crime reference 13210498168 or online via www.westyorkshire.police.uk/101livechat