Anglo has also been rocked by a boardroom row over the appointment of a new chairman. Some directors of the company opposed the appointment of Sir John Parker, the respected industrialist, because they wanted a South African to take the helm.
Headhunters have now drawn up a shortlist which is understood to include several European executives.
Securing a merger with Mr Davis's group would enable Sir Mark Moody-Stuart, the outgoing chairman of Anglo, to depart on a high note, although Ms Carroll has argued that Anglo can generate better returns for its investors by remaining independent.
The approach to Anglo comes weeks after Rio Tinto, its larger rival, scrapped a planned tie-up with Chinalco, a state-controlled Chinese company, in favour of a joint venture with BHP Billiton.
Anglo and Xstrata declined to comment last night. Glencore could not be reached for comment.
Additional reporting by Peter Taylor of The Telegram.