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.
However, there is encouraging news on the pair, with nine games to play as Burnley fight for their Premier League status.
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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And Pieters has been out with a knee problem suffered in the draw at Crystal Palace in February.
5. Rangers lead Summerville race
Rangers have the ‘advantage’ in the race for Leeds United star Crysencio Summerville this summer if they battle HSV Hamburg for his signature. (Frankfurter Rundschau)
6. Boro plot Toon raids
Middlesbrough are ready to raid Newcastle United for Jamal Lewis, and are also keeping tabs on Sean Longstaff. (TEAMtalk)
7. Mitoma speaks out on Brighton future
Brighton forward Kaoru Mitoma has admitted he doesn’t know what the future holds when his current loan deal comes to an end. The Japanese international is currently on loan in Belgium, and has claimed that his fate this summer ‘depends’ on a decision from Albion. (Het Nieuwsblad)
8. Man City consider Phillips pursuit
Manchester City could enter the race for Leeds United star Kalvin Phillips, who is also on Manchester United’s transfer radar. (The Athletic)