The Belgium international is available to leave the club before the end of the European transfer window on August 31, having spent last season out on loan at Wolfsburg.
Borussia Dortmund are understood to be interested in Origi's services, but the Liverpool Echo reports that the Reds will not consider bids of under £27m.
The 23-year-old joined Liverpool for £10m in 2014 but has spent two of his four seasons out on loan, making only 77 appearances for his parent club in that time.
Dortmund have reportedly registered their interest in the striker, but are yet to table an official bid with less than two weeks to go before the end of the window.
Fenerbahce have also been credited with an interest, while Wolverhampton Wanderers are understood to have made a £22m bid with add-ons earlier this summer, only for Origi to turn down a move to Molineux.