A man in a dark-coloured Land Rover is alleged to have approached a two-year-old girl in Chapel St Leonards.
Lincolnshire Police have said that a woman was walking with her two children and a pushchair along Trunch Lane between 4.15pm and 5pm on Monday, June 12, when the suspicious incident is believed to have happened.
A spokesperson for the force said: “DC Calley Murray would like to speak to anyone who was in the area at the time and who may have witnessed any suspicious activity.
“We would like to hear from you if you have any information that could assist the enquiry.”
Anyone who can help with the investigation should call Lincolnshire Police on 101, quoting incident number 366 of June 12.
Alternatively, contact the independent charity Crimestoppers anonymously on 0800 555 111.
Officers have also stressed to residents to always call 999 in an emergency.