In a word, no.
Should the club respond to every rumour, no matter how silly? Hell, we've had everything thrown our way by the "grapevine" bar alien abduction, so I'd sooner see LFC get on with the job at hand rather than stoop to making statements on non-issues. No other club does so I can't see why Livi should be the exception. The club's more open and honest now than at any time in its history, and I'm happy with that.