There's no way of telling yet about the takeover rumours, but the club's statement means nothing as regards the chances of an offer being made. Varney is only saying that there has been no contact or approach, something which would only happen when any consortium is ready/able to make an offer.
Like everything, it depends on the price. I think there will be genuine interest in a takeover. Championship teams with a good shot at the premiership can be bargains (eg Sunderland) - or turkeys (Leeds, unless you are good at card tricks and can get debts removed without blinking). But there seems to be a common assumption that being bought out automatically involves having more money available for investment. A takeover involves purchase of the club from the people who currently own it. Nothing more - unless the sale makes such stipulations and/or the prospective new owners make it plain that they intend to provide additional funds for players/ground development.
I'm confident Murray would only sell if he felt it to be in the club's best interests, and he has earnt our trust. But we are at a crossroads. If we fail to rebound we are back on a par with Southampton (unless they are bought), Leicester, Coventry etc (we will always be bigger/better than our former landlords). We can't compete in the premiership over the medium term unless we have bigger gates/more resources, which on the evidence of the past couple of years requires better players, which means ....
In retrospect as soon as the Valley expansion plans went on ice (for good reason, the demand just wasn't there) the club stalled, Curbs felt time was up, the applicants to replace him were not exactly high quality, and we have paid the price. In that context the club may need a fresh injection of enthusiasm - and money. It is not as if the accounts for the past year are going to make good reading.
I think we have three possible future paths: there is no sale and we get promoted back next season (leaving us where we were last time around, perhaps stronger); there is no sale and we don't get promoted (ie we're back to where we were before the play-off season); or there is a sale and it involves significant additional resources, giving us a good shot at promotion next season or the season after but with no guarantee that new owners would have the same commitment to the club as the current ones.
Just hope it is all resolved before Pardew starts to plan for next season as fresh resources would make a difference over who stays/goes and who is brought in.