Messi is currently locked in negotiations with Barcelona over a new contract with his current deal set to expire at the end of June.
The Argentine was expected to have already signed his extension after Barcelona announced in July Messi would be staying until 2021.
But, talks have dragged on and Spanish daily AS claim City have been watching the developments closely with a view to a January transfer.
Barcelona have repeatedly told fans not to worry and are still confident the deal can be reached.
‘Everything is signed. There is no need to worry,’ Barcelona president Josep Maria Bartomeu insisted.
However, City are waiting in the wings and have already held discussions with Messi’s ‘inner circle’.
Manchester City 2017/18 Fixtures
Swansea City (A) - Wed Dec 13
Tottenham (H) - Sat Dec 16
Leicester City (A) - Tues Dec 19 (EFL Cup)
Bournemouth (H) - Sat Dec 23
Newcastle United (A) - Wed Dec 27
Crystal Palace (A) - Sun Dec 31
Watford (H) - Tues Jan 2
City are prepared to smash the world-record fee Paris Saint-Germain paid for Neymar last summer and poach another Barcelona superstar.
Pep Guardiola would be delighted to be reunited with Messi who he coached in his time at Barcelona.
Messi and Guardiola helped Barcelona achieve a golden era of success with three La Liga titles and two Champions League trophies in the span of three years.
Despite the interest from England, Messi is keen to stay in Spain with his wife and family settled in the country.
The prospect of moving to Manchester would be a major upheaval for his family and Messi still feels valued at Barcelona.