Spurs allowed Troy Parrott to join Millwall on loan on Saturday, and Jose Mourinho will be keen to sign a replacement as cover for Harry Kane.
And Watford are ready to offload Deeney as one of many big earners as they prepare for life in the Championship.
The Daily Mail claim Tottenham have held talks over an initial loan deal for Deeney, who admitted he may have played his last game for the Hornets in an emotional interview following their relegation.
Deeney told Sky Sports: “We haven’t quite been good enough at both ends of the pitch and it showed again today. It’s frustrating, it’s disappointing, it’s is heart breaking for the people who work behind the scenes.
“There are a lot of people at clubs who normally get affected by relegation so we feel sorry for them. I’ll take the stick with regards what comes social media wise.
“The harsh reality of it is that some people will lose their jobs because we haven’t been good enough. As players we have to stand forward, take that and as a club and a community we go again.”
Bournemouth’s Callum Wilson has also been discussed but he would command a greater transfer fee.