Ramsey sustained the problem on Tuesday night towards the end of his country's 2-1 win over Andorra in Euro 2016 qualifying.
Despite fears over the severity of the injury, Ramsey is hopeful of lining up against City at the Emirates Stadium on Saturday.
"I'll be alright," the 23-year-old is quoted as saying by BBC Sport. "The pitch was very hard. There's no give in it so I rolled my ankle a bit.
"Hopefully it will be nothing and I'll be available for Saturday. These are the games you want to play in and I'm looking forward to it."
Arsenal are currently in seventh place in the Premier League table after three matches.