All three burglaries happened on Tuesday and all properties were ransacked.
Police said cash and jewellery were stolen.
A PSNI spokesperson said: “Detectives in Lurgan are investigating reports of three burglaries at houses in Lurgan and Waringstown on Tuesday 12th April.
“The reports received stated that a house at Colane Road in Lurgan was entered sometime between 2pm and 4pm, a house on the Banbridge Road in Waringstown was entered between 11am and 6pm and a house at Oaklands, also in Waringstown, was entered sometime on Tuesday.
“Cash and jewellery were reported stolen from the houses in Waringstown and whilst entry was gained to the house at Colane Road, nothing is believed to have been taken at this stage. All houses were ransacked.
“Detectives are investigating a possible link between the three incidents as one line of enquiry and are appealing to anyone who noticed any suspicious activity at any of these locations on Tuesday to contact them at Lurgan station on 101, quoting reference number 1177 12/04/22. A report can also be submitted online using the non-emergency reporting form via http://www.psni.police.uk/makeareport/ or you can contact Crimestoppers anonymously on 0800 555 111 or online at http://crimestoppers-uk.org/.”