France's Schneider Electric SA
The newspaper, citing two unnamed sources, reported that Schneider was in talks with public equity firms to make a bid that could top $30 billion.
A spokesman for the French company said no deal was in the works. A Tyco spokesman declined to comment.
The Post added that the company not yet determined which private equity firms it would team up with if it were to make an offer. It also said it is possible private equity bidders would work on their own, without Schneider.
A bid of $30 billion would represent a 29 percent premium to Tyco's current $23.2 billion market capitalization.
Tyco shares rose 3.5 percent to $51.24 on the New York Stock Exchange. Schneider shares were down 1 percent at 112.680 euros in Paris.
The two companies have laid out conflicting visions of what might be going on over the past month, since talk of a possible deal first emerged.
There is no plan of large-sized acquisitions now and in the foreseeable future, Schneider CEO Jean-Pascal Tricoire told investors on an April 20 conference call.
But a little more than a week later, Ed Breen, head of Tyco, said he was open to the possibility of a deal.
We always, as a management team, present to our board and talk to them about all the alternatives you can have to create long-term sustainable shareholder value, Breen said on an April 28 conference call.
A Schneider spokesman repeated Tricoire's denial on Friday.
Our CEO expressed himself clearly at the time of our earnings report on this topic and we have nothing to add, Schneider spokesman Anthime Caprioli said.
Tyco spokesman Paul Fitzhenry declined to comment.
(Reporting by Scott Malone, additional reporting by Aftab Ahmed in Bangalore and Christian Plumb in Paris; Editing by Derek Caney and John Wallace)