Widnes Local Policing Unit has received two reports of children being followed by a man.
The first incident around 8am on Monday 21 January involved a 10-year-old boy who was walking from Milton Road and onto Charles Street.
The boy noticed a man dressed in black walking behind him. He believed that he was being followed so he ran away from the scene.
The second incident at around 8.30am on Tuesday 22 January involved another 10-year-old boy who was walking with his bicycle in an alleyway between Arley Walk and Hough Green Station.
The boy reported seeing a man dressed all in black running towards him, so he got on his bike and cycled away.
Chief Inspector Simon Parsonage said: “Enquiries are ongoing to establish the full circumstances of what has taken place.
“Understandably there are some concerns from the local community regarding these two incidents and we have increased patrols in these areas to provide reassurance.
“If anyone has any concerns then they are urged to speak to a local officer.
“We remind people to be vigilant and to report any suspicious activity.”
Anyone with information which may assist the investigation is asked to contact Cheshire Police on 101, quoting IML 301155, give the details via https://cheshire.police.uk/contact/general-enquiries or contact Crimestoppers anonymously on 0800 555 111.