Sean Dyche issues injury update ahead of Norwich clash
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But the skipper, and left back Erik Pieters, could be back in contention for Easter Sunday’s game at West Ham.
Mee has missed the last four games with a hairline fracture to his fibula, suffered in the first half of the 2-0 defeat at home to Leicester at the beginning of March.
And Pieters has been out with a knee problem suffered in the draw at Crystal Palace in February.
Boss Sean Dyche said: "Ben and Erik are beginning to make progress.
"Not (available) for this week, but for West Ham, we will wait and see
“They are with the physios and sports science, and then it is how quickly they can get out with us, so there is a possibility."
Winger Johann Berg Gudmundsson is likely to be out longer than the pair, after being out since the goal-less draw at Arsenal with appendicitis, and a subsequent calf injury.
Dyche added: "It is still going to be a while yet, we are going to have wait and see."
Connor Roberts came off against Everton with a mix of a thigh issue, and a tactical change to get Matt Lowton on to “sit in there a bit more with his experience.”
And Dyche has a selection issue in the right back slot: “We want those problems and conundrums of picking the right team because usually if you have got that it means people are playing well.”