The company said circumstances surrounding the Coopers' deaths are "unclear" and that it received reports of "a raised level of illness among guests".
Nick Harris, a lawyer who is representing the group, said his clients had reported becoming unwell after recent stays at the Steigenberger Aqua Magic Hotel.
The BBC identified them as John Cooper, 69, and his wife Susan, 63, a Thomas Cook employee.
At least 20 have also reportedly filed legal claims against the hotel, and say the travel company is keeping them in the dark about what was going on.
"Other guests are saying there are 40 people ill at the hotel with vomiting and diarrhoea", she said.
Hotel management denied there was an unusual level of sickness, and, like Egyptian officials, insisted the couple from Lancashire had died from natural causes.
Dr Maged Eledawy, the head of Hurghada Hospital, earlier said Mr Cooper died after suffering a heart attack before Susan died from grief.
The pair were staying at the Steingenberger Aqua Magic Hotel, which is popular location for hundreds of holiday makers and well reviewed on online travel websites.
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West Ham also started the Premier League season with two back-to-back losses to Liverpool and Bournemouth. "It was a hard match. He feels better today and before the match he was with me", Emery said.
Mrs Elliott told Sky News she is unsure whether her sickness was caused by food poisoning or something to do with the hotel room, such as the air conditioning.
Thomas Cook said the tour operator would be offering customers alternative hotels within Hurghada from Friday onwards, as well as giving them the option to return home.
"Mum and Dad were fit and healthy, they had no known health problems", she said in a statement to British local radio station 2BR.
Thomas Cook had earlier released a statement reacting to the incident and explaining why they took the step of removing their guests from the hotel.
Kelly also added that she wanted to clear up speculation about the couple's cause of death in the national press.
Mr Fankhauser continued: "Twenty-four hours after the couple died, we had our specialists.in the hotel".
"We are supporting the family of a British couple who died in Hurghada, Egypt and we are in contact with the local tour operator", it said in a statement.
After the bombing of a Russian passenger jet flying from Sharm el-Sheikh in the Sinai Peninsula in 2015, Egypt-bound flights from Russia were halted for more than two years, hurting Egyptian tourism revenues.