Newcastle and Nottingham Forest are attempting to convince the Bees to sell the striker.
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But talkSPORT says the Bees will not consider any offers for Wissa this summer as they seek to support new manager Keith Andrews.
Forest failed with a bid in January for Wissa and have been trying to reopen talks with Brentford this summer.
But Brentford's board will not consider losing Wissa as they prepare to accept a £70m offer from Manchester United for Bryan Mbeumo.
Wissa's deal runs to 2026, with an option for another 12 months.