First, it was leaked that Joe Lewis was considering selling Tottenham Hotspur. Then an American group, Cain Hoy, said that they were interest in the club. Finally, the club denied that they were in any takeover talks.
Spurs had to make any takeover talks public so coming out and saying otherwise wasn't just a PR move. Had they been in talks, they would have had to say so, per the law. That law also requires that they follow up 10 business days later.
Earlier this month in accordance with the requirements of the City Code on Takeovers and Mergers (the "Code"), the Club was required to write to all shareholders to notify them of a possible offer for Tottenham Hotspur Limited (THFC). THFC confirmed at that time that it was not in takeover discussions with any party. We are further required by the Code to issue a statement, 10 business days following the initial announcement listing the shareholding interests of the main shareholders, which is set out in the link below. Both these actions are formalities.
That listing of the shareholders isn't particularly interesting, but it is available here.
So still not talks yet, and no real movement. If Cain Hoy really is interested in buying Spurs, they have kept it internal or informal to this point. That doesn't mean things can change and they can't engage Tottenham in takeover talks before the October 10 deadline, when they have to submit a firm bid by, but so far there is nothing happening.
In conclusion: Cain Hoy said things, Spurs are complying with the law.