Officers issued the bizarre appeal for information on Monday following a spate of “suspicious incidents” across Aberdeenshire.
The male suspect is said to stop female runners and ask for a lift on their back as he is “injured”.
Four incidents have been reported to police.
One runner was approached in the town of Laurencekirk on August 7.
And another three were spooked after being stopped on an old railway line, which is popular with fitness fanatics, between Aberdeen’s suburbs of Cults and Milltimber on August 28 and September 3.
Police said that the unusual encounters took place in the morning and afternoon and involved a middle age man, who was wearing exercise clothes.
Sergeant Andy Peerless said: “We are particularly keen to trace a male described as being around 40-60 years of age, between 5 ft5 and 5ft8, of a stocky build with grey receding hair. In each case the man has been wearing exercise clothes.
“In each case the women who have been approached say the male has been persistent in nature and behaving oddly.
“Officers will be giving particular attention to the areas in question and are taking these reports extremely seriously.”
He added: “While on the surface these incidents may appear fairly innocuous, they have made the women involved feel extremely uncomfortable and alarmed which obviously makes this a concern for us.
“Given the frequency of the incidents and the similarities between them, we are asking the public to be vigilant and report any concerns to police as soon as possible while our inquiries continue.
“Anyone with information should contact Police on 101 or contact Crimestoppers on 0800 555111 if you would like to remain anonymous.”