Distin pulled out of Sunday's 2-0 defeat at Manchester United just before kick-off through illness, but is poised to return to the squad that takes on the League One strugglers who dumped out Liverpool in the last round.
Striker Victor Anichebe is a doubt with a knock sustained at Old Trafford that saw him substituted just before the hour, while the game looks set to come too soon for right-back Seamus Coleman who has recently been sidelined with a thigh injury.
FA Cup hero Matt Smith could return from injury as Oldham go in search of another giantkilling at Boundary Park.
The 23-year-old netted twice as the Latics pulled off a major shock by beating Liverpool 3-2 in the fourth round.
But the striker sustained a shoulder problem in that tie and has not played since, only returning to training on Thursday to try and force his way into caretaker manager Tony Philliskirk's squad for the visit of the Toffees.
Fellow forward Robbie Simpson has also made his comeback from a hamstring injury and, if he can prove his fitness, may be in contention.
Oldham have also been boosted by the availability of their loanees, with Reading midfielder Jordan Obita and strikers Chris Iwelumo and Lee Barnard, from Watford and Southampton respectively, getting the go-ahead to feature.