Spurs defender is understood to be a personal recommendation from City captain Vincent Kompany and has suggested he will look to leave White Hart Lane if they miss out on top four.
City is looking for a first choice central defender to partner captain Vincent Kompany and is ready to bid for Vertonghen at the end of the season.
Vertonghen is understood to have been personally recommended to City chiefs by Kompany, his Belgium international teammate.
The pair have a good relationship and City believes they would offer a strong balance for Manuel Pellegrini’s side, with Matija Nastasic, Martin Demichelis and Joleon Lescott all failing to convince the Chilean manager this season.
City is also tracking Porto defender Eliaquim Mangala but has baulked at the 45 million euro release clause for the Frenchman, while Pellegrini is a huge fan of Real Madrid center back Pepe.
Vertonghen is seen as an attainable option and would immediately adapt to City having spent two years in the Premier League since joining Spurs from Ajax for around 9.5m euro in July 2012.
Spurs want to keep Vertonghen but expect the 26-year-old to push for a move away from White Hart Lane at the end of the season.
Vertonghen was named in the PFA team of the season in his first year at Spurs but has struggled this year. Tottenham’s defensive injuries mean he has not played with a consistent partner in central defense, while he has often been forced to play at left back.
He has previously been linked with Barcelona but is not thought to feature near the top of the Spanish giants' list of potential replacements for Carles Puyol when the center back leaves the Camp Nou in the summer.
Tottenham looks almost certain to miss out on a top four finish and Vertonghen has refused to commit his future to the north London club if it misses a place in next season’s Champions League.
“My favorite thing, what I want of course, is to play in the Champions League with Tottenham,” Vertonghen said in February. “That’s what I want so I hope we get in there this year.
Asked about his future if Spurs miss out, he replied: “I can’t say anything about that, so let’s see after the end of the season and after the World Cup.”