The right-back, who enjoyed an impressive return to the first team during Sunday's derby, is in line to equal the Toffees' European appearance record currently held jointly by Colin Harvey and Brian Labone.
Hibbert has played 18 times in European competition for the Blues, and needs just one more game to see his name added alongside those two legends.
The Huyton-born 28-year-old is expected to start in an Everton defence which will be without John Heitinga and Lucas Neill.
Neither were registered in time to take part and are ineligible.
Everton can secure qualification to the next stage of the Europa league if they beat AEK Athens, and Benfica beat FC BATE Borisov in Minsk.
Joseph Yobo, however, has not travelled with the squad to the Greek capital.
The Nigerian centre-back was forced off during Sunday's defeat by Liverpool with a hamstring injury and it will keep him out of the Group I encounter against the side he scored against at Goodison Park in September.
Teenage midfield- er Jack Rodwell has travelled, despite missing the derby with a groin strain. French striker Louis Saha has also made the journey, but continues to carry a thigh injury.
Meanwhile, Steven Pienaar has prom- ised to overcome his injury problems in order to boost Everton's season.
The South African midfielder returned from an extended spell on the sidelines to play two games in five days last week, playing 90 minutes in the defeat at Hull before producing a Man of the Match display in the derby.
The 27-year-old admits he is still not 100 per cent pain-free in the knee he injured during the 1-0 win at Portsmouth earlier in the season.
He said: 'I still feel a bit of pain, but it's going to be there for a while. So I just have to keep on playing because it's important if I want to stay fit.
'I've missed 10 games already, so it doesn't matter how many games I play in a week as long as my body can take it; I'm prepared for it.
'On Thursday (after the Hull game) my body was stiff. I had a lot of aches but that's normal. You just have to be mentally strong, express yourself and I feel okay.'
He also backed his team-mates to bounce back against AEK. 'Sometimes in football you get an opportunity to make things right quickly and this game is one of those opportunities. We want to take it.'
Pienaar believes Everton can turn derby misery into a new beginning for their worrying season.
And the 27-year-old from Johannesburg insists a run of just one win in 11 matches 'is nothing to panic about, even if we are in a mess.'
Pienaar believes he saw enough in the Merseyside derby to believe things are about to change.