Elsa Salama vanished in December 2011 after her father Tamer Salama, 41, took her from her mother Naomi Button, 43, while all three were visiting Egypt.
Ms Button, a leadership consultant from Leeds, launched family court action in England in the hope of getting her daughter back.
Mr Salama - a former teacher who lives in Manchester and has lived in Nottingham and Southampton, Hampshire - was jailed in January 2012 for breaching judges’ orders to arrange Elsa’s return to England or to reveal where she was.
He was released in December 2013 after a judge ruled that continuing to keep him in prison was no longer proportionate or justifiable.
Mr Justice Baker, the judge currently overseeing the litigation at hearings in the Family Division of the High Court in London, has been told that Elsa is thought to be living with her father’s relatives in Cairo.
He said he wanted to speak to Elsa directly via Skype or FaceTime - and had asked Mr Salama to arrange to have the youngster made available to take a call.
But Mr Salama says his relatives have refused to make Elsa available and do not want to co-operate.
Lawyers representing Mr Salama broke the news to the judge at a hearing in the Family Division of the High Court on Thursday.
Mr Justice Baker had said he wanted to speak to Elsa directly when he analysed the case at a hearing a few weeks ago.
He indicated that he wanted to gauge the youngster’s thoughts and feelings.
The judge had said an Arabic interpreter would be needed because Elsa no longer spoke English.
Mr Salama had told the judge he could arrange for his relatives to make Elsa available.
The judge said he would reconsider the case on January 20.