The AC Milan striker was loaned to Serie A side Roma on the final day of the transfer window after turning down a loan switch to Juventus.
The 28-year-old was also strongly linked to Real Madrid and the Premier League side.
"It could have ended differently," said Borriello's agent Tiberio Cavalleri to Corriere dello Sport.
"On Monday, I had a call from (Manchester City coach Roberto) Mancini saying he wanted the player (Borriello) to go to Manchester City.
"On Tuesday, Real Madrid made an approach but then (Real's Karim) Benzema said no to (a move to) Marseille and that's when Roma came into the picture."