The 32-year-old England international will head a list of summer sales with Manuel Pellegrini poised to take over at the Etihad Stadium.
Pellegrini is expected to make sweeping changes to the Citizens first-team squad, after the club already completed the high profile signings of attacking midfield duo Fernandinho from Shakhtar Donetsk and Jesus Navas from Sevilla.
Barry could leave Manchester City for as little as £4million - £8million less than what they paid Aston Villa for his services in 2009 - and that has Tottenham interested.
Andre Villas-Boas is on the lookout for a replacement for Scott Parker, who endured an injury-ravaged campaign at White Hart Lane in 2012/13, and is believed to be keen on a cut-price move for Barry.
With just 12 months remaining on his Manchester City contract, Barry is yet to be offered a new deal, and could complete a transfer to north London, as Spurs look to strengthen their squad in the hope of keeping Gareth Bale for another season at least.
Stoke City have also been credited with an interest in the player, as new manager Mark Hughes - who was responsible for bringing Barry to Manchester City - keen to be reunited with the midfielder at the Britannia Stadium.