Bedfordshire Police said it was aware of suggestions the group was in Syria but these were "uncorroborated".
Relatives raised the alarm when the family did not return home from their trip after stopping in Turkey.
The BBC has also learned a family home was raided and one member stopped at Heathrow the day before they departed.
The woman, believed to be 21-year-old Rajia Khanom, was stopped while the family was at the airport on 9 April because she was suspected of trying to go Syria.
She was not arrested, but a search then took place at her home on Spencer Road where she lived with her parents.
On the day of the search, a Bedfordshire Police spokesman said the raid took place with a warrant under terrorism legislation.
The missing family is:
It is believed Ms Khanom had links to banned Islamist group Al-Muhajiroun, which had members in Luton.
The family flew to Bangladesh on 10 April, police said, and flew to Istanbul on 11 May. They were due back at Heathrow three days later but failed to return.
They were reported missing to police by two sons, understood to be Mr Mannan's from a previous marriage, who live in Luton.
Ashuk Ahmed, who has known the family for 35 years, said people in the community had told him some of the women might have been radicalised.
He had been told they took the rest of the family with them to Bangladesh to avoid detection, he said.
In a statement, Bedfordshire Police said following the airport search and house raid there was no information which suggested any of the family were intending to travel to Syria.
"So they were allowed to travel the following day without any police intervention," the force said.
"While the suggestion is that the party's current location is in Syria, this remains uncorroborated and our enquiries are continuing."
In a statement, relatives said they were "devastated by the disappearance" and they "can only think they have been tricked into going there".
A family of 12 from Luton who went missing on a trip to Bangladesh have contacted UK relatives saying they are in Syria, sources have told the BBC.