The Chile international will be available on a free transfer at the end of the season once his contract with the Gunners expires.
City came close to signing Sanchez for £60 million in the closing stages of the summer transfer window but Arsenal pulled the plug on the deal as they were unable to sign a replacement in time.
City have maintained their interest in Sanchez, although Guardiola is understood to have concerns that the 29-year-old’s arrival midway through the season could upset the balance of his squad.
But according to Manchester Evening News, Guardiola is now ready to sign Sanchez before the end of January as he wants more options in attack.
Guardiola currently has just one fit first-team striker in Sergio Aguero as Gabriel Jesus has been ruled out for up to six weeks with a knee ligament injury.
Earlier this week, reports claimed that Arsenal would be willing to sell Sanchez to City if they received an offer in excess of £25m.
Arsene Wenger, meanwhile, has insisted that Arsenal would sign a ‘top quality’ replacement if Sanchez did leave this month.
‘This club has lost many, many big players and has always responded well,’ said the Arsenal manager.
More: Arsenal FC