Interior Ministry Secretary of State Bostjan Sefic said Slovenia could not accept Croatia's request to take 5,000, because Austria's daily limit is 1,500, the report reads.
Most migrants - many from Afghanistan, Syria and Iraq - are crossing Croatia and Slovenia to reach western Europe.
The limitation on numbers has led to a build-up of migrants and refugees on Croatia's border with Serbia.
Around 40 buses of people were backed up in Serbia on Sunday, and tempers flared between frustrated migrants and overstretched police officers.
"We are waiting here four hours on the bus," Muhammad Samin from Afghanistan told the Associated Press. "The weather is too cold. We wear lots of shirts. The children are also in the cold. No food."
The UN's refugee agency says about 4,000 migrants crossed into Slovenia on Saturday. By Sunday morning, Austria said it had allowed through around 1,000 people.
Slovenia became the main route for migrants after Hungary closed its borders to them on Friday night, citing security concerns.