The Hammers have won three of their last four games as Sam Allardyce's side sit fourth in the Premier League table, four points adrift of second-placed City.
Their flagship result in that run of form was a 3-1 victory at home to Liverpool last month, and Jenkinson - on loan from Arsenal - hopes that there will be another scalp when the champions turn up on Saturday.
"I think we've shown we can beat the big clubs already this season with the Liverpool result," he told the club's official website.
"We know what we're capable of. Man City are flying at the moment, they're a world class team so nobody is kidding themselves because we know it is going to be a difficult game."
Kickoff in East London is scheduled for 12.45pm.