A statement from Cheshire Police confirmed it had passed a file to the CPS after questioning Mr Amesbury about the incident last week.
Mr Amesbury, who represents Runcorn and Helsby, was suspended from the Labor Party last Sunday after a clip was published by MailOnline which apparently shows him continuing to punch the man, who is lying on the ground, as bystanders shout ‘Stop’ .
He was not arrested but was questioned under caution after attending a voluntary police interview last weekend.
On Friday, a spokesman for Cheshire Police said: “Cheshire Police received reports of an assault in High Street, Frodsham, at 2.48am on Saturday 26 October.
“An investigation was immediately launched and a 55-year-old man was voluntarily questioned under a police caution in relation to this incident.
“On Tuesday, October 29, a file was sent to the Prosecutor’s Office for review on Tuesday, October 29, and we await their decision.”
The CPS confirmed it had received a file but failed to give a time frame for its decision on whether to charge Mr Amesbury.
In a statement released shortly after the incident, Mr Amesbury said he had turned himself in to police and would co-operate with their inquiries while remaining an “open and accessible MP for our community”.