It once again looks like a straight fight between City and Tottenham for that all-important fourth spot in the Barclays Premier League following Sunday's 2-0 defeat at Chelsea.
"It would be a huge statement to other European clubs," Given told Abu Dhabi-based newspaper The National. "It would show we are going to be around for a long time and that we are going to be the team to watch over the coming years."
He added: "The club would be able to attract more players in the summer and keep some of the ones we already have happy.
"Everyone wants to play in the Champions League. It would have been fantasy stuff to the fans a few years ago to think City might have teams like Barcelona and Real Madrid at Eastlands. Now there is a realistic chance of it happening."
With just two wins from their last seven league games, City's title aspirations have disappeared.
However, they still have an FA Cup semi-final with Manchester United on the horizon and while fourth place does not bring a trophy, the prize is hardly insignificant.
"We started the season wanting to win the league, you've got to aim high," said Given.
"It looks like we're going to fall a bit short of that. The next best thing is to get in the Champions League. Nobody wants to finish fourth, they want to finish at the top.
"But as the season has progressed we've dropped too many points and it looks as though the most realistic chance is the Champions League."