The England international was forced to sit out his fifth successive game after picking up a thigh injury during the international break in September.
Reds captain Steven Gerrard broke the deadlock in the Merseyside derby before Everton centre-half Phil Jagielka levelled in injury-time.
Liverpool manager Brendan Rodgers is hoping to have Sturridge available for the tricky trip to Swiss champions Basel in the Champions League on Wednesday.
And Sturridge, who moved to Liverpool from Chelsea in 2013, is optimistic that he is close to making a return to competitive action for the Reds.
— Daniel Sturridge (@D_Sturridge) September 27, 2014
Sturridge netted an impressive 21 goals in 29 Premier League games last season, despite spending six weeks on the sidelines.
The former Manchester City youth graduate has scored 32 goals in 46 Premier League outings since his £12m switch to Anfield.
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