Levy is willing to give Tim Sherwood an extended chance to land the job fulltime after the departure of Andre Villas-Boas yesterday.
The Daily Mail says Levy and football director Franco Baldini have compiled a lengthy list of alternatives to Sherwood. Southampton manager Mauricio Pochettino is highly rated, Ajax boss Frank de Boer has also been discussed and Basle chief Murat Yakin is viewed as another possibility.
Fabio Capello, who has close links to Baldini, and Guus Hiddink are obvious contenders but both would be short-term appointments.
Italy coach Cesare Prandelli and Celta Vigo manager Luis Enrique are other options favoured by Baldini. Sherwood, however, has been given the chance to prove his credentials.
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