Boro seem certain to reject Downing's demand because they do not want to sell their prized asset to a club that constitute rivals in the relegation fight at the foot of the Premier League.
Plus, Tottenham have done little to win friends at the Riverside by making what Boro chief executive Keith Lamb has called a "derisory" offer believed to be in the region of £6 million.
It is understood that an offer in excess of £10m has now been submitted, but with Boro valuing Downing at £15m, Spurs will have to raise their bid significantly before allowing him to leave less than a year into a five-year contract on Teesside.
Boro Chairman Steve Gibson made it clear he had told Spurs counterpart Daniel Levy that Downing was not available for transfer on Sunday.
"I can confirm we have received an offer from Spurs for Stewart Downing and I can also confirm we have rejected that offer," said Gibson.
"I've spoken to Daniel Levy and told him categorically that their interest is not welcome.
"I've also told him we will not entertain any further offers for Stewart or, for that matter, any other senior member of our squad. The same applies to Tuncay and it also applies to Gary O'Neil.
"I repeat: none of our senior players will be leaving the Riverside Stadium this month. We've got a talented group of players and it's time for us to knuckle down and focus on the job in hand. As far as we're concerned, this is now an end to the matter."
Downing's Boro colleague, David Wheater, is desperate for his team-mate to resist the temptation to be reunited with Jonathan Woodgate at White Hart Lane.
"The manager says he wants to keep our best players and that's what you have to do if you want to move up the league," the England Under-21 defender said.
"I hope he wants to stay because being a local lad he loves the place and the club and hopefully he wants to do well.
"Do I see the day when Stewart might move on to a big club? You never know.
"That's what you want to do in your career – play for the best clubs and win trophies – so if we don't start doing it here maybe he might want to move on in the future. He will obviously want to be the best he can be at football.
"It's just like someone working in an office working their way up to be a manager. We just want to do the best we can. But hopefully he doesn't leave yet – we need everyone scoring goals at the moment."