Officers are searching for Owen Buck, 23, of Andrew Street, who is wanted in connection with allegations of rape, stalking, assault and criminal damage.
The offences were reported between November 2021 and January this year, say Lancashire Police.
As well as his hometown of Preston, Buck also has links to Blackburn.
But police believe he might have fled to Scotland, where he has links to the North Ayrshire area, including Irvine, Stevenston and Dalry.
He is described as 5ft 8in tall, of medium build with dark brown hair and brown eyes.
T/DC Joe Harper, of Lancashire Police, said: “Buck is wanted for a number of serious offences.
“Our enquiries suggest he is in Scotland and I would encourage people to share our appeal.
“If you can help with our investigation, please come forward.”
Anyone with information can contact police on 101 or email [email protected] quoting log 0788 of February 7.