It opened the door for Chelsea to make their move for the Spaniard – who joined Brighton late in last summer’s window for £15.4m from Getafe.
Carragher, speaking on the Overlap ahead prior to the Premier League kick-off this weekend, has questioned the wisdom of Chelsea’s move.
"I don't understand that one. You [Chelsea] bought Ben Chilwell for £50million and then you’re trying to get another left-back.
"You didn’t want him a month ago, you want them now?"
Chelsea already have Chilwell and Marcos Alonso on the left – although Alonso is expected to complete a £7m switch to Barcelona shortly.
Chilwell had his injury problems last term and Cucurella – who can play anywhere down the left, including left side of the back three, will add a fresh dynamic to Thomas Tuchel’s men as they prepare to compete for the Champions League and the Premier League titles.
Earlier this window, ahead of Cucurella’s proposed switch to City, Carragher said. “Since Pep has been there, Man City have lacked a real outstanding left back.
"It has always been a position for different players. Joao Cancelo has done as well as anyone.
"I'm sure Pep would like a left footer in there and Oleksandr Zinchenko has gone to Arsenal.
"Man City usually spend £40million to £50million on full backs since Pep came. Like any transfer, you have to see if he plays well and is he worth it?
"He looks a classy player in the Brighton shirt and they play similar type of football to Manchester City. I'm sure he would be a good signing for Man City and a player they possibly need and give competition for Cancelo."