Boro are searching for a new manager after the departure of Tony Mowbray yesterday.
Former Middlesbrough midfielder Souness, ex-Sunderland boss Martin O'Neill, Nigel Clough, Gary Megson, Danny Wilson and former Stoke manager Tony Pulis are in the running after Mowbray's three-year reign was brought to an end following Boro's appalling start to the season, says the Daily Mail.
Mowbray's assistant Mark Venus is in temporary charge of the club. They play Doncaster Rovers at the Riverside on Friday night.
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