Justin Mellersh, 46, had legal custody but his children had been missing since early 2010. He is in Turkey fighting to bring the bodies back to the UK.
He said he believes an internet report that they have already been buried and, if correct, wants the bodies exhumed.
The BBC has contacted the Turkish Embassy in London but officials are yet to comment on the case.
'Extreme thing' The children's UK-based family appealed to the Turkish president earlier who was in Hampshire during a state visit.
Mr Mellersh, whose parents live in the New Forest village of Minstead, near Lyndhurst, said he wanted to bury his children there.
Speaking to BBC News from Turkey, he said: "According to a website apparently the children have been buried, they have had a funeral. It's not something I can confirm but I suspect it is true.
"I think it is only fair and morally right that these children should go to their father, to their next of kin.
"My children should be where I decide and certainly I should be able to see them before they are buried.
"There is a possibility they could be exhumed and it is a very extreme thing and hard for me to go through that.
"If I was asked if I was prepared to do that I think I would say yes."
'Political problem' He had earlier said a Turkish court had ruled the bodies should be transferred to the custody of their mother's relatives in Turkey.
The children grew up in Hampshire before the family moved to Germany. Their mother, Elke Mellersh, 45, was a German citizen.
Mrs Mellersh was wanted by Interpol on suspicion of child abduction after she and the children went missing near Bremen, in Germany, in February 2010.
He had called on the UK Government to intervene in the case.
Meanwhile, the children's cousin, Natasha Mellersh, appealed to President Abdullah Gul by holding up a placard showing pictures of the children while he visited a naval cemetery in Gosport, Hampshire, on a three-day state visit.
She stood at the cemetery's gate but the president's cavalcade did not stop.
She said: "We're here as we wanted to raise the issue with the president, to make him aware of this escalating from a legal issue to a political problem."
The bodies of the children and their mother were found in a farmhouse in Soke near the Aegean coast, western Turkey, on Friday.