The former Liverpool goalkeeper missed last night's preseason friendly against Borussia Monchengladbach. The match finished 2-2, marking the Bees' final hit-out before next week's Premier League opener against Nottingham Forest.
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Hakon Valdimarsson stood in for Kelleher, whose injury is described as a minor "knock".
Discussing Gusto Nunes' absence, Bees manager Keith Andrews said: "Exact time scale, I'm not entirely sure.
"Certainly not in the Kevin (Schade) and Caoihmin territory of short-term. It will be more significant than that, it will be weeks."