The French international only joined the North London side over the summer from Toulouse, but has endured a tough start to life as a Spurs player.
After some initial bright displays, the 25-year-old found himself sidelined through injury, which halted his progress.
He has since returned to action, but a lack of cover at the heart of the club’s defence has seen him used as an emergency centre-back during a difficult spell for the Lilywhites.
Roma have been alerted by these issues, and are hopeful that they can take advantage of the situation to steal Capoue away.
The Stadio Olimpico-based side’s manager Rudi Garcia is believed to be a big fan of the former Ligue 1 star after witnessing his talents first hand during his time at the helm at Lille.
Capoue’s future at White Hart Lane appears to be uncertain under new boss Tim Sherwood, despite him having been a favourite of Andre Villas-Boas, who was recently sacked.
The midfielder may be tempted by a move away from the club in the winter, with the 2014 World Cup looming.
Roma are also rumoured to be keen on fellow Spurs enforcer Sandro.