He Zhengsheng, a Beijing lawyer for the family of Neil Heywood, said talks with lawyers representing the convicted killer Gu Kailai had brought "initial results and some consensus".
He added: "We are making all efforts to achieve a final outcome."
Mr Heywood's murder was at the centre of China's most embarrassing political scandal in decades, with Gu's husband, Bo Xilai, dismissed from his post as Chongqing party chief and stripped of other political positions.
Former politician Mr Bo will stand trial tomorrow on charges of corruption and abuse of power that appear limited in scope to secure his co-operation and minimise damage to the Communist Party's image.
His wife was given a suspended death sentence last year after confessing to poisoning Mr Heywood.
Mr Heywood was survived by a Chinese wife and two children, who lived in a gated community in a Beijing suburb and attended international schools, although their current whereabouts is unknown.
Li Xiaolin, a lawyer with ties to Gu's mother, had previously said the Heywood family was seeking up to £5 million in compensation.
But Mr He, the Heywood family's lawyer, refused to provide details about the amount.