On-loan striker Lukaku, 20, was stretchered off just after Liverpool's opening goal at Anfield after colliding with Everton team-mate Gareth Barry while defending a Liverpool corner.
Following the match, which Everton lost 4-0, Toffees boss Roberto Martinez was pessimistic about the injury, revealing that Lukaku had his ankle in a cast to protect suspected ligament damage.
However, in a statement on the club's official website, Martinez revealed that the injury is less serious than doctors feared.
"There is no ligament damage and the injury is not as bad as we first thought," said Martinez. It will be a case of weeks rather than months."
Belgian international Lukaku has impressed during his time on loan at Goodison Park from Chelsea, scoring nine goals in 20 appearances to help the club maintain a challenge near the top of the table.
However, last night's heavy defeat left them in sixth place and four points behind their fierce rivals, who are fourth.