The newspaper has spoken to a girl who has been approached several times by adults who offered her up to 3,000 kronor per month if she changed home, and moved in with them instead.
On one occasion, such an approach was made on Migration Agency premises.
Social workers based in Uppsala, 70km north of the Swedish capital Stockholm, confirm that they have heard rumours of such cases.
Foster homes in Sweden can receive up to SEK 19,000 per month per child.
Svenska Dagbladet has previously found cases where heavily indebted people have taken in as many as five refugees as foster children, without social services having carried out proper checks on those running the homes.
Ingrid Burman is the chairman of the social affairs committee at the local council in Uppsala. She tells the paper that the authority needs to improve the way it checks the suitabilty of foster homes.
Last year, over 35,000 unaccompanied minors applied for asylum in Sweden.