Officials in Brussels confirmed today that they had requested detailed information following a number of complaints.
In a statement, the council said one of the complaints focused on land deals around Celtic Park in the east end of the city.
The Commission said it had not yet opened a formal investigation and that the information was being analysed.
It said no conclusions could be drawn at the moment.
A spokesman for the city council said: “A complaint was made to the European Commission on historic land deals around Celtic Park.
“The Commission is legally obliged to investigate all such allegations and the council was happy to provide information on these transactions.”
Responding to the news, Celtic issued a statement rubbishing the complaints as “preposterous”.
It read: “Celtic Football Club operates to the highest standards and with the utmost integrity. At a time when the Club is committed to investing in and improving areas around Celtic Park - not only for Celtic supporters but for the benefit of the local community - it is sad that these baseless accusations have been raised with the European Commission.
“Any suggestion that Celtic has been the beneficiary of state aid is preposterous. It is as ludicrous as any suggestion that we have benefited from soft loans from our bankers. The historic transactions referred to were negotiated with the Council on commercial terms at market rates.”
It added that the club would assist the Commission fully but would not be deterred from its work “to improve our local area”.
The Commission is also investigating whether allegations of cut-price deals between the government and some Spanish football clubs, including Real Madrid and Barcelona, constitute “state aid”.