Bidve was shot dead in Salford as he walked with friends from his hotel [AFP]

British police are offering a reward of of nearly $78,000 for information leading to the arrest and conviction of the killer of an Indian student.

Anuj Bidve, 23, was shot in the head at close range in the northern English city of Salford on Monday.

"It is an extremely unusual, savage and motiveless attack, an absolutely horrific crime, which is why we are taking the step of issuing it [the reward] a bit earlier than we normally would," Detective Chief Superintendent Mary Doyle said.

"We absolutely understand the need to take whoever is responsible for this off the streets."

The microelectronics student was with a group of friends when he was shot after a brief conversation with a man who approached them.

Police say they are treating the murder as a hate crime which may have been racially motivated.

Arrests

A 16-year-old boy and two 17-year-old boys arrested over the murder have been released on bail pending further inquiries. Two men, aged 19 and 20, remain in custody.

Police have yet to find the murder weapon, believed to be a small handgun.

According to a Facebook page set up in Bidve's memory, he "was killed for not answering a simple question - 'What's the time?'".

But police have not yet disclosed what was said between the killer and his victim.

Bidve, from the western Indian city of Pune, was studying at nearby Lancaster University and had been on a short break in Manchester with eight Indian friends when he was shot.

Police said the students were walking from their hotel towards the city centre when they became aware of two men on the other side of the street.

A white male walked across the road and after a brief conversation with the victim produced a gun and shot him at close range, before running off. Bidve died in hospital a short time later.