There had been reports that Scottish champions were keen on a loan signing while Brendan Rodgers was in charge, and in terms of Rangers there was the Steven Gerrard factor - the Ibrox boss having been a team mate of the striker.
Realistically, however, it was always unlikely due to the player's wages.
When Sturridge signed a new five-year deal in 2014 it bumped his wages up to more than 120,000-a-week. Spotrac report that he was earning £6.76million-a-year.
The 29-year-old arrived in Turkey yesterday to sign for Trabzonspor. He is set to take a substantial wage cut but still earn £2.8million a year.
There has also been interest from Marseille, Eintracht Frankfurt, Real Betis and Atalanta, as well as DC United in MLS.