The Spanish goalkeeper injured his wrist while on international duty earlier in the month and was forced to sit out of the Reds' 1-0 win over Reading last Saturday.
It was initially feared that Reina would miss the trip to Goodison Park, but Rodgers said that the medical team will assess his progress over the new two days.
"Pepe is back in training, so that's good news," said Rodgers. "He's working well and we'll assess him over the next 24/48 hours."
Reina joined Liverpool in 2006.