Southampton are reportedly keen to appoint their new manager within the next 10 days.
Last week, the Saints revealed that they had terminated the contract of head coach Claude Puel "with immediate effect".
Puel replaced Ronald Koeman as head coach of the English club last summer, and the 55-year-old went on to lead them to an eighth-place finish in the Premier League table.
Puel also steered Southampton into the final of the 2016-17 League Cup, but the board decided to relieve the Frenchman of his managerial duties.
According to the Daily Echo, Southampton are wary of entering pre-season without a head coach, and the South Coast outfit have set themselves a '10-day deadline' to put a new manager in place.
Frank de Boer and Mauricio Pellegrino are said to be the two favourites to step into the position.
