Mani Dad was living with his Polish mother Leyla Dad in Kielce, Poland, when he disappeared early this year.
He is thought to be in the UK with his British father, property dealer Zayn Dean, 47, also known as Dholtana Dad.
Ms Dad, 33, said Costa coffee shops were among Mani's favourite haunts and asked customers to look out for him.
Ms Dad, who has launched family court proceedings in a bid to find her son, said she had spoken to Mani by telephone several times and he told her he had visited Costa with his father.
"He loves Costa. We often used to take him when we lived in England," said Ms Dad.
"I would urge Costa staff and customers to look carefully at the pictures and let police know if you think you've seen them.
"Zayn is a big guy. He'd be talking on the phone. Mani would probably be playing on a computer."
Ms Dad said she thought the pair could be living in a village.
The family lived in Kettering, Northamptonshire, and Bedford before moving to Poland.
Ms Dad, who uses her middle name, Paulina, said Mr Dean, whose family is from Pakistan, grew up in Bolton and Bradford, and also had links with Birmingham, Luton, Bedfordshire, Essex and London.
She said she could not find words to describe her pain.
"I know Mani's with his dad but I'm sure he's not going to school and he's missing me," she said.
"I have to find him. I just don't know what to do."
Her solicitor Katherine Res Pritchard, of Dawson Cornwell, said: "Someone, somewhere must have seen Mani.
"We need to find him and make sure he is safe. He needs to be reunited with his mother."
A woman whose seven-year-old son has vanished with her estranged husband is appealing for staff and customers of a coffee chain to be on the alert.