The allegations emerged after videos by fans posted on the video sharing website, YouTube, appeared to show soldiers in uniform interacting with fans while singing about proscribed loyalist organisations.
It was said to have taken place during an Armed Forces Day event when Rangers played Stenhousemuir at Ibrox Stadium last month.
Police Scotland and the Army launched investigations into the match that took place on September 28.
But yesterday a force spokeswoman said: "Following a full inquiry by Police Scotland, a report on the circumstances was submitted to the procurator fiscal and the military. At this time the inquiry is completed.
"However, if new information does come to light, it will of course be acted upon."
The Crown Office said: "We have not as yet received a prosecution report in respect of any specific individuals and as such there are currently no ongoing proceedings in relation to this incident."
The Ministry of Defence could not confirm if any disciplinary action had been taken against armed forces members, but said it planned to carry on with events at Ibrox and other clubs.
The Crown Office said the document did not recommend the prosecution of any individual suspects.