On paper, it makes sense: One of the industry's most powerful agency networks, known for its own voracious appetite for acquisitions, has been caught in a downward trajectory severe enough that it may now find itself prey.

"Twenty months on from the collapsed merger talks with Omnicom, we believe an acquisition of Publicis is now a feasible prospect," Jérôme Bodin and Pavel Govciyan, research analysts at Natixis, Paris, wrote in January. "Publicis is now an extremely attractive target, from both a financial and strategic standpoint. The decline in its share price … has left the group's valuation extremely low. Meanwhile, the slump in the euro relative to the dollar makes it an appealing target for an American player."

Natixis said Publicis' stock dropped 12.6 percent in the last year, selling at a 26 percent discount to other ad agencies.

One major obstacle is Publicis' strong-willed chief Maurice Lévy, whose vow to relinquish power next year is met with some skepticism. "It would most certainly have to be a hostile takeover since I don't see Maurice Lévy allowing it," observed Seth Alpert, managing director, AdMedia Partners.

However, Natixis' Bodin insists "a hostile bid would be risky but has every chance of success, even in the ad agency segment." Insiders control just under 20 percent of shares, down from 22 percent at the time of the Omnicom merger. (Publicis, of course, is no stranger to hostile bids, making its own for U.S. agency True North in the mid-1990s.)

Another problem for potential buyers is the huge price tag for Publicis, with a market cap of $13.1 billion. Some industry insiders estimate a purchase price of $17 billion, a 25-30 percent premium. Bodin asserts a deal could primarily be financed in shares.

In terms of likely strategic acquirers, Bodin makes the case for Omnicom and Dentsu Aegis Network: Omnicom and Publicis had already struck a deal where neither partner had to exchange cash; the transaction was backed by key shareholders and it received regulatory clearances. As for Dentsu Aegis, he points out the two companies already know each other: Dentsu used to own 15 percent of Publicis, and the Japanese giant is looking to expand quickly and a tie-up would bring creative assets, with strong positions in the U.S., Europe and Asia.

Lévy told Adweek Publicis is not for sale; Omnicom CEO John Wren declined comment. Tim Andree, executive chairman, Dentsu Aegis Network, was also tight-lipped about future expansion but said he'd be hesitant about taking on Publicis with its current challenges.

An investment observer concurs: "A sale seems like an enormous stretch. Publicis is a bit of a mess right now. In a bizarre way it's like a multibillion-dollar fixer-upper."

More specifically, observes Pivotal senior analyst Brian Wieser: "Its problems go back to the Omnicom merger; Publicis management have acknowledged they got distracted by it. They've made mistakes in underinvesting in their creative agencies so they can make acquisitions, which have created a political situation alienating talent. On the media side, Publicis has been punching under its weight," losing big media accounts such as Walmart, Mondelez, Procter & Gamble and Coca-Cola. (Lévy is attempting to change course, having announced a massive corporate reorganization last fall.)

However implausible a sale scenario is for Publicis, there is still a lingering "never say never" hesitation to rule anything out after the French network announced a staggering, surprise $35 billion deal with Omnicom in 2014.

"An [Publicis] acquisition is certainly a provocative idea but a real stretch," said AdMedia's Alpert. "If you look at the big players, they all make acquisitions, but I don't think they make bet-the-farm deals like this. Still, I didn't expect to ever hear that Omnicom and Publicis were going to merge."

This story first appeared in the Feb. 22 issue of Adweek magazine. Click here to subscribe.