But Boro chief executive Keith Lamb says the club are desperate to hang onto one of their star performers.
He told the Evening Gazette: "We have had absolutely no contact from Tottenham or any other club about Stewart."
Boro are expected to land a top-class striker during the January window, with Heerenveen ace Afonso Alves tipped to arrive in a £14million deal.
But the Gazette claims Boro boss Gareth Southgate wouldn't need to sell Downing in order to fund any big-money deals.
Downing's Riverside deal has more than two years to run, but talks have so far failed to produce a contract extension.