Weimann still has to agree terms, and his agent has hinted that other clubs are ready to make offers, but Villa are confident a deal will be done.
Lambert said: "Andi has been exceptional. He is a natural finisher who knows where the goal is, but his work-rate is second to none.
"That was the thing that struck me when I came here and first started working with him. He has a natural hunger and desire to get better and that can take you a long way.
"Success doesn't go to his head; money wouldn't go to his head.
"Whatever happens you are always going to get the same player with the same drive and ambition."