The Times reported Mr Coupe had been sentenced in his absence to two years in jail in what Sainsbury's described as "an historic commercial dispute".
The charges relate to a joint venture that Sainsbury's set up with a local businessman in 2001.
Sainsbury's said that Mr Coupe was not employed by the company at that time and he had never met the complainant.
Sainsbury's said the complainant, Mr El Nasharty, bought out its interest in an Egyptian joint venture it had with him in 2001 with cheques that were dishonoured.
It said Mr El Nasharty was now claiming that Mr Coupe was in Egypt on 15 July 2014 and seized those cheques.
But Sainsbury's said this was an impossibility: "Mike Coupe was in London carrying out his normal duties that day. In September 2014 Mike Coupe was convicted, without notice of the proceedings against him and in his absence, in an Egyptian Court.
"We have taken all necessary steps to appeal against these groundless claims and will continue to do so."
It added that its legal team were handling the matter and it did not think the issue would have any  material, operational or financial impact on the company.
Sainsbury's has rejected any allegations against its chief executive Mike Coupe in a legal row in Egypt.