Fire crews from Penwortham were called to reports of an abandoned motorbike on fire on Tulketh Crescent at around 11pm on April 19.
They arrived to find the bike "well alight".
A spokesman for Lancashire Fire and Rescue said: "We attended what looks like a suspicious motorbike fire late last night.
"The bike was completely destroyed and unfortunately the number plates and the Vehicle Identification Number were also damaged during the fire so we have been unable to trace the owner."
Nobody was injured during the blaze.
Anybody with information regarding the incident can contact police on 101.