Hostile takeover bids are at their highest level in more than a decade, according to Thomson Reuters. The latest example came Monday, when France’s Sanofi-Aventis (SNY) said that it will take its $18.5 billion offer for Genzyme (GENZ) straight to company shareholders.

At a macro level, this should represent a huge opportunity for private equity. The buyout business flourished in the 1980s as a direct response to corporate raiders, and most PE deals over the subsequent decades have been done with the consent — and often activity participation — of company management. Couple that with the PE market’s record amount of dry powder, and it would seem that there are plenty of deals for the making.

But not Genzyme.

The first problem is price. Sanofi-Aventis will almost certainly need to jump its $69 per share offer by at least a couple of dollars, as evidenced by the fact that it’s currently trading above $71 per share. That means private equity firms would need to come up with at least $7.5 billion in equity (assuming 60% leverage). Possible via syndication, albeit difficult without the type of sponsor-friendly debt terms that sparked the 2006-2008 buyout boom.

So let’s assume private equity firms somehow cobbled together the cash. Even then, they still won’t buy Genzyme. Not because of its underlying financials or management, but because private equity firms simply cannot compete in auctions for big biotech.

A company like Sanofi-Aventis can create hundreds of millions of dollars in savings via consolidation and R&D synergies. Private equity firms don’t have the same abilities, which means they would virtually be forced to overpay by a comparable amount. I’m not saying that private equity won’t overpay — happens all the time — but rarely do they do so when it’s so obvious to all involved (particularly when not competing against one another for bragging rights).

Need proof? I asked Thomson Reuters to run the largest PE-sponsored pharma deals of the past decade. Some of what came back were drug manufacturing, marketing and packaging companies. Once you strip those out, you are left with just three deals valued at over $1 billion: Nycomed, Warner Chilcott and Axcan Pharma. None of those was anywhere close to $10 billion, let alone to what Genzyme would cost.

“Private equity can get involved is it’s a small specialty pharma company that strategics don’t want, but not something like Genzyme,” says the head of health care investing at a large buyout firm. “We simply cannot compete.”