The London Evening Standard says Brentford management are confident securing the pair to new deals.
Both players currently are recovering from serious injuries and their deals will expire in June.
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And Brentford plan to hand both players short-term arrangements.
Veteran defender Mee, 34, suffered an ankle fracture in February's 4-2 defeat at West Ham.
Dasilva, meanwhile, returned from a six-month hamstring injury in February only to suffer a serious knee ligament setback. He has since undergone surgery.