Around 30 police officers are searching woodlands after a possible sighting of a prisoner on the run.
Tayside Police warned the public not to approach Lee Cyrus, 47, who disappeared on day release from North Sea Camp open prison in Boston, Lincolnshire, earlier this month.
He is serving a life sentence for robbery.
Police are investigating two violent attacks in the Perth area in the last fortnight, including the sexual assault of a woman by an intruder who attacked the victim in her own bed.
Police said a "suspicious" male was spotted by an off-duty officer by the A90 Perth to Dundee road at around 7.20am. He lost sight of the man when he ran into woods at Kinnoull Hill.
Specialist search officers and dogs have been hunting the area.
A police spokeswoman said:
Cyrus, also known as Ivan Leach, failed to return to prison on Tuesday October 9 and police believe he may have travelled to the Tayside area.
The man spotted today was described as being of medium build, with a round face and clean shaven. He wore muddy, dark-coloured waterproof trousers and top and a beanie hat. He was carrying a rucksack-style bag, police said.
Tayside Officers are investigating the sexual assault of a 23-year-old woman as she slept in her home in the Bridgend area of Perth. The intruder threatened her before the attack at around midnight on Monday October 15.
The assault followed a nearby robbery the previous night in which a woman was attacked in her home.
The man who carried out the sex assault was wearing a dark-coloured beanie hat, a grey jumper and khaki green waterproof trousers with a black belt. He was also wearing khaki green boots and spoke with an English accent.
Police said they are keeping an open mind about whether the robbery and the sexual assault are linked and did not comment on whether Cyrus is considered a suspect.
Lancashire Police want to speak to Cyrus about reports that a man fitting his description approached two schoolgirls for sex last week.
The man spoke to the girls as they sat at a bus stop in Lancaster Road in Preston city centre on Wednesday October 17 at about 6.30pm.
He made sexual remarks and encouraged them to participate in sexual activities, police said.
The girls boarded their bus and then reported the incident to police.
At that time the offender was described as having stubble and wearing a black top, black shorts, carrying a rucksack.
Cyrus was jailed in 2005 for the robbery of a 90-year-old woman at her home in Ribbleton, Lancashire.
Members of the public are warned not to approach him.
Anyone with information as to his current whereabouts, or anyone who has seen him since he absconded should contact Lincolnshire Police on 101. Information can also be passed anonymously to the charity Crimestoppers on 0800 555 111.