It has been reported that the chanting occurred during Stoke’s visit to Oakwell on Saturday.
Northern Ireland manager Michael O’Neill made his debut as Stoke City manager at the game, which was won 4-2 by the Potters.
Creggan born footballer McClean was regularly booed during the game was also targeted with chants about the Pope and the IRA.
The game took place the day before Remembrance Sunday, where the UK remembers the contribution of the military during the world wars and other conflicts. A minute’s silence was held before the game.
A number of players wore poppies on their shirts during the match.
McClean has not worn a poppy during his many years in English football, citing the actions of the British Army in his native city on Bloody Sunday.
He has regularly been targeted with abuse by football fans for the decision and disclosed that he has received death threats in the past.
It has been reported that referee Jeremy Simpson included the abuse in his report of the game and the FA is investigating as a result.
Speaking last year Republic of Ireland international McClean defended his decision not to wear the poppy.
“I know many people won’t agree with my decision or even attempt to gain an understanding of why I don’t wear a poppy,” he said in a statement released through Stoke City.
“I accept that but I would ask people to be respectful of the choice I have made, just as I’m respectful of people who do choose to wear a poppy.”
The Irish PFA and major anti-racism group released a joint-statement demanding an investigation into anti-Irish racism.
A joint statement from Ged Grebby and Paul Kearns (Show Racism the Red Card), Garrett Mullan (Show Racism The Red Card Ireland), Stephen McGuinness (Irish PFA) read: “Football Associations must respond with investigations of anti Irish racism.
“The FA have announced that they have investigated and warned James McClean for use of language arising from a post he put up on Instagram in which he referred to supporters who were abusing him.
“This statement is a joint call from Show Racism the Red Card Ireland, Show Racism the Red Card UK and the Professional Footballers Association of Ireland to both the Football Association in England and the Scottish Football Association to have a more robust approach to abuse faced by players like James McClean and managers such as Neil Lennon.
“Racism on the basis of colour, nationality, religion or ethnicity is not acceptable and all within the game have a responsibility to respond appropriately.
“James McClean has stood in solidarity with team mates who have experienced racism and spoken out. We stand in solidarity with James McClean, Neil Lennon and all those who experience racism.
“We call on both the Football Association in England and the Scottish Football Association to investigate all incidents of anti-Irish discrimination.
“We also call on both associations to invest funding in anti-racism education to help both supporters and young people understand the dangers and the impact of racism.”