Cambiasso, a former Argentina international, claimed five Serie A titles at previous club Inter Milan where he also won the Champions League in 2010.
"For me, it's like another cup," he told the BBC on Thursday.
"When you start another season you have an objective, and this is the objective for us.
"For me, winning a cup or winning the league with another team is the same now as having the possibility to save Leicester in the Premier League."
Leicester, promoted last season, will have their work cut out to avoid an immediate return to the second tier.
The Foxes are rock-bottom of the 20-team table, seven points adrift of 17th placed Sunderland and without a league win since January.
"I understood when I signed for Leicester it's not an easy job to stay in the Premier League," he said.
"It's a difficult situation but I think we have our chances to win matches. There's a quarter of the Premier League left.
"I think some people think for Leicester all is finished. But I'm sure, because I watch my team mates every day, we can save Leicester and stay in the Premier League."
Nigel Pearson's side face West Ham United at home on Saturday.
(Reporting by Toby Davis; editing by Martyn Herman)
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