The Sun says Dyche would be willing to commit to the end of the seaso should Tottenham choose to remove current caretaker manager Igor Tudor.
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Tudor is yet to earn a point since taking charge after the dismissal of Thomas Frank.
And Spurs management are discussing hiring Dyche to replace Tudor in order to avoid the drop.
As it stands, Tottenham sit just one point outside the bottom three on the Premier League table.
Dyche is available after being sacked by Nottingham Forest, having taken charge after the previous dismissal of Ange Postecoglou this season.