Capoue, 26, is understood to be close to agreeing to personal terms and negotiations are also ongoing with Stambouli, although an agreement with the 24-year-old is still some way from being reached.
Sky sources also understand that Watford have agreed terms with Greece international Jose Holebas but have not yet finalised a transfer fee with his current club Roma.
France international Capoue joined Spurs from Toulouse under previous head coach Andre Villas-Boas and featured consistently for the Portuguese, but he struggled to maintain a first-team place under successors Tim Sherwood and Mauricio Pochettino.
Capoue has made just 19 Premier League starts in two years and did not appear in a Tottenham match-day squad in any competition after January 24 this year.
Stambouli, meanwhile, was signed from Montpellier last summer instead of a loan deal for Alex Song, who joined West Ham, but the former France U21 failed to hold down a regular place in Pochettino’s starting eleven too, making just four Premier League starts.
The pair are set to become Watford’s fifth and sixth signings of the summer having been promoted from the Championship last term. The Hornets have already signed Austria defender Sebastian Prodl, goalkeeper Giedrius Arlauskis and attacker Matej Vydra on a permanent deal from Udinese.
Capoue and Stambouli are set to follow the recent departures of Paulinho to Chinese club Guangzhou Evergrande and Lewis Holtby to Hamburg, as Spurs trim down their squad ahead of the new season.
Sky sources understand that strikers Emmanuel Adebayor and Roberto Soldado, defenders Younes Kaboul and Vlad Chiriches, and winger Aaron Lennon are also available to other clubs at the right price.