The Irish Independent says Origi cannot join Dortmund on loan without an obligation from the German club to buy him.
Dortmund remain in talks over signing Origi before the end of the month.
Liverpool's initial £27 million valuation was considered too high by Dortmund, who would prefer to take the Belgian on a season-long loan.
But, with just two years remaining on Origi's contract, Liverpool will loan out the 23-year-old only if there is an agreement that Dortmund buy him at the end of it.
Liverpool do not want Origi's value to drop while he is playing elsewhere and leave open the prospect of him returning with only 12 months left on his deal next year.