The man, who was captured on camera, was seen grinning with his arms out of a car window, as the vehicle overtook the bicycle on October 8.
The man, dressed in an orange high visibility shirt and a dark-coloured beanie hat, was the passenger in a grey Vauxhall Astra.
Staffordshire Police has asked anyone with information to contact police quoting log number 710 of October 8.
South Staffs Police tweeted: "#APPEAL: Do you know this man? We'd like to speak to him in connection with an incident on Radford Lane in #Wolverhampton on Tues 8 Oct. A cyclist was pushed into a hedge by the passenger of a grey Vauxhall Astra. Please DM @StaffsPolice quoting 710 of 8 Oct with any information."