"It seems that there was a dispute between the two brothers about money. This seems to be credible information coming from the British police," the public prosecutor in Annecy, Eric Maillaud, told news agency AFP.
"The brother will have to be questioned at length. Every lead will be meticulously followed,” he said, adding that it is too early to draw conclusions.
Another French police source said the brother of victim, named in British media as 50-year old Saad al-Hilli, presented himself to British police on Thursday to proclaim his innocence and cooperate in the probe.
On Wednesday, al-Hilli, his wife and his mother-in-law were found dead with gunshot wounds to their heads inside their car at Chevaline near Lake Annecy, a popular tourist spot.
A local cyclist, Sylvain Mollier, was shot and killed nearby. It is believed he inadvertently came across the shooting.
The bodies were found by a British cyclist who had served in the British Royal Air Force.
The slain family’s seven-year old daughter is currently in hospital with a bullet wound to a shoulder and a fractured skull.
Her four-year old sister survived underneath her dead mother’s skirt and was not discovered until eight hours after police sealed off the crime scene.
Maillaud said the traumatised girl was questioned on Thursday night but was unable to give any more details.
French authorities are due to carry out autopsies and DNA tests to formally identify the victims.
The family’s neighbours in England said al-Hilli was an engineer and identified the other victims as his wife Iqbal, who was carrying an Iraqi passport, and his mother-in-law, who had a Swedish passport. The couple's daughters were named as Zainab, aged seven, and Zeena, aged four.
The French President, François Hollande, and the British Prime Minister, David Cameron, both said authorities will do their utmost to solve the crime.