An official source later confirmed her statement.
Shafik's daughter May Shafik, told Reuters that authorities had come for him at his home and sent him to Cairo. "They said they will deport him to Egypt", May said.
Shafiq - the last prime minister of Egypt's Mubarak era - announced late last month that he was planning to run in the presidential elections scheduled in 2018.
According to his lawyer, Shafik was arrested in the United Arab Emirates earlier on Saturday and deported to Cairo after he recently announced plans to run for president in the 2018 elections.
Shafik's lawyer on her Facebook page also said he had been taken from the family home. Egypt's foreign ministry said it was not responsible for the case.
She said Shafik had been prevented from leaving the UAE in previous days but had then received assurances that he could travel freely.
Shafik was once considered close to former President Hosni Mubarak.
"We did not arrest him and we did not receive any requests from the prosecution to arrest him or bring him back".
However, Shafiq's family is still in the UAE, said an unnamed official source cited in the ENA report.
Shafik narrowly lost to Mohamed Mursi of the Muslim Brotherhood in Egypt's 2012 election before fleeing overseas.
If Shafiq does run for the presidency, he is seen as a strong potential opponent of President Abdel Fattah al-Sisi, who is expected to run for a second term next year.
Egyptian pro-government media and talk shows, which had immediately come out against Shafiq over his bid, criticized the former air force commander again on Sunday. They provided no evidence.
It is the chief prosecutor's prerogative to investigate the complaint and, depending on his decision, refer Shafiq to trial.
Egypt has long accused the broadcaster of being a mouthpiece of the Brotherhood, which it denies.
"I don't think that he would take such a big political risk of insulting his hosts of over five years, who effectively gave him refuge while he was facing criminal charges in Egypt. We presented him with every facility and generous hospitality despite our severe reservations about some of his positions", Gargash said.
His supporters dismiss criticism over rights abuses and say any measures are needed for security in the face of an extremist insurgency that has killed hundreds of police and soldiers in the last four years.
But his government is fighting a stubborn Islamist militant insurgency in the Sinai region and has also enacted painful austerity reforms over the past year to revive the economy but that critics say have dented his popularity.