The cat received significant injuries during the attack on or near to Weldbank Lane at around 10am on Sunday, 26 February, say police.
The owner of the dogs then reportedly spoke aggressively to the cat's owner before leaving the scene.
Police are now trying to find the man pictured in the images in connection with the incident.
A spokesman for Chorley Police said in a post to their Facebook page: "We’d like to speak to the man [in the CCTV still] in connection with a report that two dogs had attacked a cat in Chorley.
"At around 10am on Sunday 26 February 2017, we received a report that a cat had been attacked by two dogs on or near to Weldbank Lane, causing it significant injuries.
"A man who was with the dogs is then believed to have spoken aggressively to the cat’s owner before leaving the scene.
"We believe the man shown in the still may have important information which could help with our investigation."
Anybody with information is urged to contact police via e-mail PCSO 7395 Laura Jones on [email protected]