Jose Mourinho's men lost Jan Vertonghen earlier in the transfer window and have so far failed to replace the Belgium international, while City have seen Nathan Ake and Ruben Dias arrive for a combined fee of £105m, pushing Stones further down the pecking order.
Tottenham have rotated between Eric Dier, Davinson Sanchez and Toby Alderweireld in central defence so far this season, while youngster Japhet Tanganga has struggled with injury issues.
According to the Daily Mail, Spurs would have to pay £20m to make the deal permanent in a year's time. However, Stones is believed to be happy to stay at the Etihad Stadium and fight for his place.
The Athletic also understand that any such move 'does not appear likely'.
Tottenham have also been linked with Antonio Rudiger in recent weeks, but the Germany international is instead closing in on a move to Serie A side Milan as exclusively revealed by 90min. Milan Skriniar is also unlikely to move to north London.
26-year-old Stones hasn't played for Pep Guardiola's side since the opening day victory over Wolves and has had mixed fortunes since joining the Catalan's revolution four years ago.
Stones was signed for £47.5m from Everton back in 2016 and, despite playing a pivotal role in Guardiola's first title-winning campaign, the Englishman has failed to progress due to injuries and a lack of form.
The former Barnsley man has won two Premier League trophies, an FA Cup and three League Cups since swapping the Toffees for the Citizens. The rise of a number of other English centre backs has also seen Stones drop out of Gareth Southgate's England set-up.
Any deal could hinge on the future of Eric Garcia, who has been strongly linked with a move to Barcelona, while Spurs have recently confirmed the loan deal of Ryan Sessegnon to Bundesliga outfit Hoffenheim.