Title-hopefuls City have kept just two clean sheets in the Premier League this season and following Vincent Kompany's latest injury setback it is understood they will attempt to sign a new centre-half in the January transfer window.
Reports over the weekend claim the Etihad Stadium outfit have set their sights on Van Dijk and are weighing up a January bid for the Dutchman, while both Liverpool and Manchester United have been linked with the past.
Prior to Saints' win over Everton at the weekend the defender was asked about previous speculation regarding his future but told the Mail he was "focusing on Southampton now" and "not thinking" about any potential move.
However, City could well test Southampton's resolve in January but it will take a big bid to convince the south coast club to sanction a sale.
Saints paid a fee in the region of £13million to land the 25-year-old from Celtic last summer and he is under contract until 2022 after signing an extension in May, meaning any potential suitor will have to come up with a huge offer to prise Van Dijk away from St Mary's in the winter transfer window.