Southampton manager Mauricio Pochettino is the favourite to take charge at Spurs following the departure of Tim Sherwood.
Ajax boss Frank de Boer - who previously claimed Spurs had enquired about his availability - is also in the running.
Former Liverpool manager Rafa Benitez, David Moyes and Michael Laudrup have also been linked with the role.
Sherwood was sacked this morning despite leading Spurs to sixth place in the Premier League.
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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.