However, Chief Inspector Rich Kirven has stated that the matter will be left for the Football Association.
"We have been working with the FA and the football club to progress the matter appropriately. Having reviewed the circumstances of the incident it has been agreed that the matter will be dealt with by the FA rather than considering any criminal proceedings," said Kirven.
"There has been no complaint received from the player involved or Hull City Association Football Club at this time. While we appreciate that some people may have found the behaviour displayed at the game on Saturday offensive, Humberside Police will not be taking any further action."
Pardew is expected to receive a suspension from the FA later this week.