The Bayern Munich manager has agreed a three-year deal to replace Manuel Pellegrini at the end of the 2015/16 Premier League campaign.
Cole played at Old Trafford for over seven seasons and won five Premier League titles, the Champions League and two FA Cups before he spent a season at City in 2005/06.
The former United striker recalled when Guardiola went to City on trial near the end of his playing career before he went on to become one of Barcelona’s most-successful managers.
“I’m still glad that Guardiola’s coming to England, though, and I’ll be interested to see who is in charge of Manchester United while Pep’s on the other side of Manchester,” Cole wrote in his Yahoo Sport column.
“Louis van Gaal has a three-year contract and we have to respect that, but everyone is talking about who will be next in line and when that will be.”
Guardiola has won three La Liga titles, two Bundesliga crowns, the Champions League twice and two Copa del Reys during his managerial career so far.
City host Premier League title rivals Tottenham Hotspur in Sunday’s late kick-off in the Premier League at the Etihad Stadium.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news