The England international has fallen out of favour at the Etihad Stadium in recent times, with new manager Manuel Pellegrini appearing to prefer captain Vincent Kompany, Matija Nastasic and Martin Demichelis as central defensive options.
Interest in the 31-year-old has been high for some time, but Spurs are hopeful that they can fight off Besiktas and Monaco to tie up a temporary transfer in the coming weeks.
Lescott is thought to have no long-term future at the Sky Blues, with an extension to his contract – which expires at the end of the season – not on the club’s list of priorities.
Tottenham chief Tim Sherwood is believed to have been told that he will have minimal funds to work with during the current transfer window, despite cover at the heart of his backline being needed.
With Younes Kaboul and Jan Vertonghen injured, the North London side are short of options in the centre of their defence, and Lescott is seen as a good option to strengthen.
Sherwood is also attracted to his experience, with the ex-Everton man having helped City claim the Premier League title in 2012.