A campaign was set up on behalf of Bradley Lowery, of Blackhall Colliery, Hartlepool, after doctors said his neuroblastoma could not be beaten.
Friends had hoped to set a world record for most cards received by one person.
However, Guinness said it did not monitor the category "due to the negative impact" on the postal service.
Envelopes and parcels have been flooding into Sunderland fan Bradley's local community centre with members of the public helping to open the deliveries.
It follows a fundraising campaign in which £700,000 was donated to pay for treatment in the United States.
After being told by doctors his cancer had grown and treatment would only give him more time, the money will now go towards the Bradley Lowery Foundation which aims to help other youngsters diagnosed with the disease.
His mother Gemma said: "It means Brad is going to leave a little bit of a legacy and that means a lot to us.
"Obviously it's heart-breaking what's happening. He's going to leave a name behind and hopefully help other children who are in the same position."
Family friend Lynne Murphy said: "We're getting cards from all over. It's so overwhelming for his family that everybody is thinking of their little boy.
"Just from the Post Office cards that have come through we've hit 234,000.
"Then in the parcels there are boxes of cards [which will take the total past 250,000].
A Guinness spokeswoman said it was "an amazing achievement for a very special cause", but added the organisation would not verify the record attempt.
A terminally ill five-year-old boy has received 250,000 Christmas cards from across the world.