Downing, 23, is unsettled at The Riverside and told boss Gareth Southgate this week he was considering his future.
A product of the famed Boro youth academy, Downing is ready for a fresh challenge and would welcome a move down south to White Hart Lane.
Former Spurs chief Martin Jol targeted Downing during his time in North London.
And chairman Daniel Levy has now given Spaniard Ramos the nod to make his move.
Tainio, 28, has been in and out of the side under Ramos - who also considered using out of favour England keeper Paul Robinson as bait to land Downing.