The boy was approached by the older man at Demesne Field at around 7pm on Monday June 10.
Police said the man asked the little boy to accompany him to the shop. The child refused and ran off.
The male is described as being approximately 5ft 10in tall, of slim build with brown skin and short, spiked, dark hair.
He spoke with a foreign accent and was wearing black and blue tracksuit bottoms, a white and blue t-shirt and skinny shoes.
Police would like to hear from anyone who witnessed this incident or has information in relation to it.
Constable Rainey, Craigavon Response, said: “It is important that this incident is looked at in perspective however all parents should speak to their children about the importance of keeping safe and not speaking to strangers.
“In this instance the child did the right thing and made his way home straight away. We are conducting enquiries to ascertain the identity of the male and his business in the area.
“If you would like more advice on stranger danger and talking to your children, or have information in relation to this incident please contact police in Lurgan on 0845 600 8000.”