Toure could be set to replace Andrea Pirlo at the MLS side after the Italian announced his intention to retire at the end of the season, according to Paul Hetherington of the Daily Star Sunday.
The midfielder signed a one-year contract extension at City in June and has previously said he wants to finish his playing career at the Etihad Stadium, per Jonathan Smith at ESPN FC.
However, Toure has barely featured this season, making just two substitute appearances in the Premier League and one start in the Carabao Cup, per WhoScored.com.
Despite his reduced playing time, the 34-year-old has still impressed on the rare occasions he has been used this term, as this stat from the UNILAD Football Twitter account shows:
However, it is difficult to see Toure forcing his way into the team on a regular basis, such is the quality Guardiola has at his disposal.
Kevin De Bruyne, in particular, has been in stunning form. Football writer Liam Canning believes the Belgian is comfortably the best player in the Premier League:
A move to sister club New York City FC would see Toure link up with former City team-mate Patrick Vieira and may be enough to tempt the midfielder when his contract expires.
Director of football Txiki Begiristain and assistant coach Mikel Arteta watched the centre-back during his side's 2-1 victory, with City keen to bring in another defender because of Vincent Kompany's ongoing injury problems.
The Belgian is out with a calf problem, and Guardiola has said he does not know when he will return, per Smith.
WhoScored.com highlighted just how much football the City captain has missed in recent seasons:
City's preferred centre-back pairing this season has been Nicolas Otamendi and John Stones, and they have formed a strong partnership.
The club has conceded just four goals in nine Premier League games this season, and the pair were particularly impressive in the win over Burnley, according to Goal's Sam Lee:
Diakhaby is just 20, a tall and powerful defender, capped at under-21 level by France and has European experience from his time at Lyon.
While he can't offer the vast experience of Kompany, he is a highly promising talent the club could be looking at as a potential future partner for Stones.