The Telegraph says any potential suitors for the England international will have to meet Liverpool's £15million valuation.
Sturridge has another year remaining on his contract and could stay on at Anfield and leave next summer on free transfer.
Sevilla pushed to sign Sturridge in January, but fancied his chances in England.
The plan was to play well at West Brom and force his way back into England set-up ahead of the World Cup, but his injury curse struck again.
A number of Turkish sides have also been linked with the player, but Fenerbahce's interest has firmed up.