Drogba, 33, Anelka, 32, fellow striker Salomon Kalou, 26, and full-back Jose Bosingwa, 29, are in the final year of their Chelsea contracts.
But AVB insists he is under no pressure from owner Roman Abramovich to cash in on the £60million quartet while he still can.
Villas-Boas said: "We won't need to sell these players. Apart from Anelka, we have offered them contracts and talks are on-going, "Even if we get to January with no agreements, their loyalty will not be questioned. We'll try to reach an agreement but the important thing is for the team to defend its interests on the pitch."