A cover (12) is configured to be used with a liquid container for realizing a drinking device in conjunction with the liquid container. The cover (12) is particularly designed to prevent fluid communication therethrough in a default condition, and to allow fluid communication therethrough in an actuated condition. To that end, the cover (12) includes a gasket (30) and a cover body (20) accommodating the gasket (30), the cover body (20) comprising a liquid passage area (21) and a sealing rim (22). In order for the cover (12) to be leakproof to a high extent under all circumstances in which it is not desired to retrieve liquid through the cover (12), the gasket (30) has at least one structural feature (34) configured to secure sealing contact of the gasket (30) to the sealing rim (22) of the cover body (20) in the default condition of the cover (12).