The left back has not played in the first team since the Reds' win over Crystal Palace on Oct. 5 due to a knee injury, but is in line to be included Saturday.
The Spaniard has not featured for the Reds since their 3-1 win over Crystal Palace on Oct. 5 because of a knee problem.
However, Rodgers, whose side sits five points behind Premier League leader Arsenal ahead of Fulham's visit to Anfield, is hopeful that the 27-year-old fullback will be fit in time to face Martin Jol's men.
"We're just waiting on Jose," Rodgers told the Liverpool Echo. "He has trained and his knee is much better so we'll be hoping he will be available for the weekend. That's something we'll assess in the next 24 hours. It will be great to have Jose back."
Enrique moved to Anfield in 2011 following a four-year spell with Newcastle United.