The note was left in a post box at the L6 Community Centre in Everton.
Local Labour councillor Gerard Woodhouse posted a picture on Twitter to raise awareness of the need in his area.
In the letter, the child writes: "Dear Father Christmas. Can you help?
"Can we have a home for Christmas? Mam wants us to be all together. Can you give us some food and can I have just a nice doll for Christmas? Thank you."
The letter appeared when the team at the community centre began decorating for Christmas.
They left the post box in the cafe for visiting children to post their Christmas wishes.
Speaking on Premier's News Hour, Dr Naomi Maynard from Feeding Liverpool, a Christian charity tackling hunger, spoke of her unease at seeing the note.
"It's a heart breaking letter to read," she said. "When I first read it I almost wasn't surprised - this is a day to day reality for those with struggles who are regularly asking questions 'where is food coming from? Am I going to have breakfast this morning?'"
She did however hope some good would come from the letter.
"The response from the community has been fabulous, an outpouring of love. There's actually lots of great work already happening in Everton so hopefully, this letter might be another thing that brings more attention and more support."
Encouraging Christians to be motivated to help those in their communities, Dr Maynard said: "You might have a neighbour next door who doesn't have the same amount of money to celebrate the birth of Christ so I think what we'd be encouraging people to think how you can be generous to those around you, could you invite a neighbour for Christmas lunch who might be by themselves? Could you make up a special Christmas hamper for someone in need?"
The L6 centre team is trying to help the family and may put them up in a hotel on Christmas Day.
The children currently live with a relative.
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