It depends the meaning of Football in your country.
In China,足球 means soccer。A famous star :David Beckham
5 Mart 2015
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美式足球 or 美式橄榄球 are both correct and exact.
橄榄球 is correct but not exact because rugby is 橄榄球 too.
The thing is that most Chinese people don't familiar with 橄榄球, so we can't tell American Football from rugby. That's why they are both called 橄榄球 here.