While there's no public jailbreak for iOS 7.1 at the moment, that doesn't mean it's impossible to jailbreak. According to well-known iOS hacker ih8sn0w, his iPhone 4s running iOS 7.1 is already jailbroken.
The claim comes almost a week after iOS hacker Winocm posted a video on YouTube
demonstrating an untethered boot on an iPhone 4 running iOS 7.1. Unlike Winocm, who uploaded a video to demonstrate the jailbreak