Downing's agent Ian Elliott insists nothing can happen until Tottenham make their interest official by lodging a bid with Boro.
Elliott told Sky Sports News: "He's very, very flattered by Tottenham's interest in him.
"They play the type of football he would like to be involved in.
"If the interest was firmed up he would be interested in talking to them - but we can't take it any further.
"It's between the two clubs. Once they have agreed a deal, we can look at it and see if it's something we want to do.
"Stewart's a great professional - he gives everything to Middlesbrough.
"He's a local lad and if he left it would be with a heavy heart - but sometimes you need to move on to better your career."