The Chilean international was a transfer target for City manager Pep Guardiola as the Premier League leaders were keen on bringing the 28-year-old to the Etihad in the summer transfer window.
However, the deal did not take shape and Arsenal were forced to pull the plug on an agreement to sell Sanchez to City after they failed to sign Thomas Lemar from AS Monaco on deadline day.
The former Barcelona man has less than a year left on his contract at the Emirates and has decided not to sign an extension. Arsene Wenger has already admitted that Arsenal could allow Sanchez to leave the club in the mid-season transfer window.
Given, who played for the Manchester outfit between 2009 and 2011, believes City will always make room to sign a quality player like Sanchez.
"I think, obviously a club that is a size of Manchester City, will always look to strengthen. I think if a player like Sanchez is available, then they will be interested. There is always room for a player like Sanchez because of his qualities," Given told IBTimes UK.
Guardiola currently has the services of Sergio Aguero and Gabriel Jesus as the first-choice strikers in the squad. Sanchez's ability to play anywhere in the front three will only increase competition for a place in City's starting XI, if he decides to swap the Emirates for the Etihad.
Given stressed that it is important to have a strong squad in order to compete in the domestic and European competitions.
"With Jesus and Aguero, the competition for that place is very very strong. So, where he would fit into the squad is another question for Guardiola. That's his job to pick the team, to pick the right players in the right positions," the ex-Newcastle United goalkeeper explained.
"Probably going back to when Manchester United won the treble in 1999, they had four centre forwards. You got to compare the schedule in the Premier League and Champions League, which brings more problems for you."