The Parkhead club say there were "inconsistencies" between the words spoken by the Rangers striker and the subtitles used by the satellite broadcaster.
Celtic have called on Sky Sports to investigate.
The interview was broadcast on Monday and Sky Sports claimed Morelos said he had been subjected to racial abuse on and off the pitch in Scotland.
Morelos referenced the most recent Old Firm game in which he was sent off.
In a statement issued on Tuesday, Celtic said: "Translations provided to Celtic Football Club have shown inconsistencies between the words spoken during the interview broadcast and the subtitles used by Sky Sports.
"In particular, and most concerning, while the broadcaster used the following subtitle on screen: 'Afterwards it was very frustrating to hear the crowd screaming at me. They were saying offensive and racist words.'
"Mr Morelos does not use these words anywhere within the extended interview which has been broadcast across Sky’s platforms.
"Celtic FC has asked Sky Sports to clarify their position on this matter."
Celtic added in their statement: "Celtic, a club open to all since its inception, abhors racism. Our consistent stance is that wherever racism exists it should be tackled head on. Celtic will always investigate any report of racist behaviour and take appropriate action. This is a standard which all clubs should meet."
A spokesperson for Sky Sports said: "We are aware of concerns raised about the content of the interview with Alfredo Morelos, while we are checking those we have removed the material from all our platforms."