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.”
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