Sky Sports News HQ understands Kenny Miller was arrested earlier this month and Rangers manager Mark Warburton has pledged his support to the forward, who is waiting to find out if he faces criminal charges.
The Scottish Sun reported the former Scotland international's arrest came after a row in a wine bar in the aftermath of Rangers' 5-1 Old Firm defeat to Celtic on September 10.
Warburton would not comment on what he labelled a "judicial matter", but said the club is behind fully behind Miller and confirmed he will be available to play at Aberdeen on Saturday, live on Sky Sports 1 HD.
"From our point of view, we give the player 100 per cent support," said Warburton. "Kenny is a top class pro. You've seen from his performances, you've seen from how many times I've picked him this season, that won't change.
"I have absolutely no doubts about Kenny Miller on or off the pitch."
A Police Scotland statement said: "A 36-year-old man was arrested and is subject of a report sent to the Procurator Fiscal in reference to an incident on Saturday, September 10."
A Crown Office spokesman said: "The Procurator Fiscal at Hamilton has received a report concerning a 36 year old male in connection with alleged incidents on 10 September 2016. The report remains under consideration."
Miller played 63 minutes of the defeat at Celtic Park before being replaced with his team trailing 3-1.
He is currently in his third spell with Rangers and has scored 99 goals for the club, including two this season against Dundee and Motherwell.