The Burnley couple tragically died on Tuesday while staying at the Steigenberger Aqua Magic in the Red Sea resort of Hurghada.
The all-inclusive holiday had been booked through Thomas Cook, where Mrs Cooper was a "loyal and long-standing" member of staff. The company has since removed other families from the hotel after "high levels of illness" were reported among other guests there.
Peter Fankhauser told Sky News: "We have no real evidence what caused the deaths, but what I can promise is at Thomas Cook we are doing everything to support the family and to support the Egyptian authorities... to get to the bottom of it and to get to the cause.
"There is no evidence that it is a carbon monoxide poisoning. We have no evidence, but I don't want to rule out anything before I really know the cause."
Mr Fankhauser continued: "Twenty-four hours after the couple died we had we had our specialists in the hotel. They took probes of the food, of the hygienic systems, of water, as well the air conditioning systems, and all those probes are now in Egypt.
"They are now examining and testing the probes and we support them in doing that, but that takes about 10 days."