The main hurdle to overcome is the price. According to the Sun
, Boro want £15 million for Downing, who signed a new five-year contract last February.
As such, Boro are in a position to demand what they like and, if Tottenham are to get their man, it may involve a swap deal with Gareth Bale.
However, Redknapp will be loath to lose his Wales international left-back, and it is thought Jamie O'Hara could be used as part exchange instead.
On the possibility of losing key players in the January transfer window, Boro manager Gareth Southgate said: "I'd love to say x, y or z are untouchable but I can't. I've got to be honest and say certain players would be sold.
"They would have to be exceptional offers but there are certain clubs with exceptional money.
"We'll fight to keep our best players but are not in a position to say they are untouchable when there is an offer too good to turn down.
"The majority of clubs in this division will feel the same way in January."
Another winger being linked with Tottenham is Sunderland's Kieran Richardson.
The Mirror reports that Richardson has emerged as an £8m target, but that Spurs face stiff competition for his signature from Bolton.