Victim Ally MacLay was in fancy dress following a Halloween party at a Glasgow nightclub when the alleged incident took place at about 1am on Sunday morning.
It is believed that the three Scottish international players are due to be questioned by detectives, along with a capped Scotland Sevens player.
Police inquiries are continuing into the alleged incident in Great Western Road, Kelvinbridge.
The players had been at a separate Halloween function with Glasgow Warriors team-mates.
Maclay, 29, a player for Glasgow Hawks rugby club and a coach at his former school, the High School of Glasgow, suffered a fractured eye socked and other injuries.
The Warriors quartet had earlier been seen inside the nightclub, but witnesses said one of them was ejected.
A Police Scotland spokeswoman said: "We received a report of a 29-year-old man being assaulted outside a takeaway shop in Great Western Road, Glasgow, on Sunday morning.
"Inquiries are continuing and no arrests have been made."
A Glasgow Warriors spokesman said: "At the moment it is speculation and we don't comment on speculation."
MacLay, who has previously played in Hong Kong and Australia said via a club spokesman he would leave the investigation to the police.