The father, who died with his wife and mother-in-law, may have been in a dispute with his brother, a French public prosecutor has said.
The bodies were discovered earlier this week in the Haute-Savoie region.
Eric Maillaud, who is leading the investigation, said police will question Saad al- Hilli's brother "at length".
He said: "This seems to be credible information coming from the British police. Every lead will be meticulously followed."
But, Mr Maillaud warned against drawing early conclusions saying it was difficult to imagine a feud could "pass from a financial dispute to a quadruple murder".
Detectives hope that post-mortems will shed light on a theory that the shooting was carried out by a hitman.
The latest comments came after President Francois Hollande said French authorities would do their "utmost to find the perpetrators".
Mr Hollande, who is visiting the UK, joined Prime Minister David Cameron in pledging to get to the bottom of the tragedy. M Hollande said: "We will do our utmost to find the reasons."
Saad al-Hilli, 50, who was originally from Iraq, was shot in the head alongside his dentist wife, named by neighbours as Iqbal, and a woman believed to be her mother.
The couple's four-year-old daughter, named as Zeena, was found alive in the car under the bodies of her relatives around eight hours after the massacre, which also saw a passing French cyclist, Sylvain Mollier, 45, shot dead.
The al-Hillis' seven-year-old daughter, believed to be called Zainab, was in a medically induced coma in Grenoble University Hospital after being beaten around the head and shot in the shoulder during the attack.
Three of the four who were killed were shot in the head, but M. Maillaud said: "I won't say it was professional, what I will say is it was tremendous savagery."
One of the family's neighbours, in Claygate, in Surrey, said he would alert police to something Mr al-Hilli said before going on holiday. But Jack Saltman added: "I am not prepared to speak about it."