Farzana Ameen, her husband Imran and their five children, aged between five and 15, travelled from Bradford on a one-way ticket to Turkey and were last seen on October 5.
West Yorkshire Police have launched a missing persons' inquiry and say that lines of inquiry are currently being progressed with the Turkish authorities.
"The indication is that they have got a one-way ticket. We know from previous experience that Turkey is a gateway to Syria and also Iraq," said Russ Foster, West Yorkshire Police Assistant Chief Constable.
The 40-year-old couple's relative has said that Farzana had contacted her brother in Pakistan yesterday and had also recently travelled to the country with her mother, who has health issues, to leave her in the care of relatives there.
"She has spoken to him. She sent him messages, and apparently the last message was: whatever she's doing she's doing the best for the kids," Arshid Siddique said.
"I hope they haven't got into Syria and then there's still a chance. I don't give a damn about [the parents] now to be honest, but it's the kids and what they've put them through," he added.
It is believed they entered Syria to join the Islamic State (ISIS) terror group.
British police and security services believe at least 700 potential extremists have travelled from the UK to Syria, and around half are thought to have returned home.
Many of those fleeing the UK to Syria go to territories under the control of ISIS, which has seized large parts of the war-torn country and in neighbouring Iraq.
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