Danjuma, who has been seeking a return to the Premier League this month, was all set to join the Toffees before next week's deadline.
But Spurs have hijacked the move, with the expectation now that the former Bournemouth player will join the north London club.
Danjuma is understood to have completed a medical at Goodison Park, but the paperwork is yet to be finalised, says the Daily Mail.
And that has given Spurs an opportunity to move for Danjuma.
Danjuma is due to arrive at Tottenham's training facility later on Tuesday with a view to undergoing a medical and signing off on the deal.
The forward is now on course to become Tottenham's first signing of the transfer window.