The rebuttal came after the commission received a number of complaints relating to the purchase of land around Celtic Park and asked for detailed information from Glasgow City Council and the Scottish Premiership club.
Its training complex was built on the grounds of the disused Lennox Castle Hospital in East Dunbartonshire.
Celtic dismissed the claims as "ludicrous" and said: "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 - 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. The club will assist the commission fully with the process and will not be deterred from our work to improve our local area."
A Glasgow City Council spokesman said it had assisted with the investigation and added: "The council was happy to provide information on these transactions."
A Scottish Government spokesman said: "We are aware of these allegations and we are working with the relevant parties to help the commission to investigate this case consistent with our role to ensure public funds in Scotland are used in compliance with EU state aid regulations."
He said the transaction between NHS Greater Glasgow and Clyde and Celtic is not part of the EC investigation, but added: "We are also aware of it and are discussing it with the relevant parties."
The commission is already investigating allegations that Real Madrid and Barcelona illegally received Spanish state aid.