The European Commission has asked for details from the football club and Glasgow City Council after receiving a number of complaints about the purchase of land around Celtic Park.
The Commission has not opened a formal investigation but is analysing information.
Celtic said the purchases had been made on "commercial terms at market rates" and it will assist the Commission fully.
A spokesman for the Glasgow City Council said: "The Commission is legally obliged to investigate all such allegations, and the council was happy to provide information."
A statement on Celtic's website 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 Commission.
"Any suggestion that Celtic has been the beneficiary of state aid is preposterous."
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."