A report by the BBC claimed the pair were about to receive an official invitation to play in the League next season with all 72 clubs voting on the proposal on Friday.
"This is absolute rubbish," Burns told BBC Five Live's Sportsweek. "We have a regular board meeting this Thursday and Celtic and Rangers are not on the agenda."
The BBC had reported that Burns met with Celtic shareholder Dermott Desmond and Rangers supremo David Murray last week in Scotland.