With Sturridge having fallen down the pecking order at Anfield, a number of clubs are said to be interested in his signature during the January transfer window.
Liverpool have allegedly set an asking price of £30m - which continues to put off his admirers - but Inter remain keen on taking the England international to San Siro.
However, according to the Liverpool Echo, the Merseyside giants have not given a positive response to Inter's terms of a loan fee and paying Sturridge's wages in full.
Liverpool's stance could potentially change later in the month but as it stands, it is being suggested that Jurgen Klopp is not prepared to do without the player's services unless the club agree a fee with an interested party.
Sturridge - who is closing in a return from injury - has made just five starts and nine substitute appearances in all competitions this season.