A $94 billion financial behemoth is keeping the market on tenterhooks about its next move.

Europe’s largest insurer, Allianz SE, is in the early stages of evaluating a variety of potential acquisition targets as deal-hungry Chief Executive Officer Oliver Baete scans the market for growth, people with knowledge of the matter said. Those on the list range from Switzerland’s Zurich Insurance Group AG and the U.K.’s RSA Insurance Group Plc to Hartford Financial Services Group Inc. in the U.S. or, going further afield, assets in China, they said.

Allianz is working with a few advisers informally in exploring options, but deliberations are at an early stage and may not result in a deal, the people said, asking not to be identified as the discussions are confidential. A spokeswoman for the firm said Allianz would consider acquisitions where the target is a “fit” on strategy, culture and price, with its board jointly taking the decisions.

An abundance of capital and returns crimped by low interest rates have prompted rivals to turn to acquisitions, with France’s Axa SA beating out Allianz to seal a $15.2 billion deal for XL Group Ltd. this year. That deal prompted speculation that the German giant, facing a lackluster stock performance this year, could target Zurich Insurance, worth about $46 billion, to bolster earnings, reap cost savings and be more competitive in key markets.

“The strategic rationale is compelling” as their businesses are complementary, James Shuck, an analyst at Citigroup Inc., said in a note to clients. “Any deal would be unprecedented in the industry, transforming global competitiveness.”

Even if Allianz were to pay a 20 percent premium over Zurich’s share price, the transaction could still boost the Munich-based firm’s earnings by 10 percent, and offer an additional 10 billion euros in capital synergies, Shuck estimated.

Allianz, whose shares have dropped about 5 percent this year, hasn’t made any formal approach to Zurich about a merger, the people said. Baete’s focus is on implementing the “renewal agenda” that he put into place shortly after taking the helm in 2015, the firm’s spokeswoman said.

The German insurer may need to look elsewhere for a willing partner, with Zurich executives including Chief Executive Officer Mario Greco publicly opposing big-ticket deals. Other targets Allianz has looked at include Australia’s QBE Insurance Group Ltd., Bermuda firms Argo Group International Holdings Ltd. and Aspen Insurance Holdings Ltd., as well as London-based Aviva Plc and the asset-management arm of Sweden’s Nordea Bank AB, the people said.

Representatives for Zurich, RSA, Hartford, Aviva, Aspen, Nordea Bank and QBE declined to comment, while spokesmen for Argo didn’t respond to a call or email.

Baete is concerned about being left behind by both Axa and American International Group Inc. — which scooped up Validus Holdings Ltd. for $5.4 billion this year — and is keen to explore a transformative deal, according to the people. The 53-year-old, who’d also previously expressed his willingness to pursue takeovers, remains keen on bolstering his defenses in the property and casualty sector and the U.S. market, they said.

The German-born CEO appeared to signal anew his appetite for mega-deals after he told the Financial Times last month that Allianz would be open to a “merger of equals.” Though Baete didn’t confirm the speculation that has linked Allianz with Zurich Insurance, and noted that the prospect of paying a high premium was unattractive, his comments were interpreted as a sign of interest. The German firm’s spokeswoman said Baete was merely explaining the circumstances under which Allianz may consider large deals in the interview.

“Strong balance sheets and lack of growth tend to make you look more externally around M&A,” Arjan van Veen, an analyst at UBS Group AG, said in an interview. But large deals, even when they “make sense,” pose significant hurdles, he said.

Those may be some of the concerns dogging Allianz Chairman Michael Diekmann, Chief Financial Officer Giulio Terzariol and board member Helga Jung, who may be more hesitant about pursuing a big deal, the people said. M&A isn’t the main priority, and Allianz is focused on operational improvements at present, Terzariol said in an interview last month.

Baete himself has ruled out any hostile takeovers. An unwilling seller would complicate any pursuit — and bump up the price.

Zurich’s top executives have already signaled that the firm won’t prove an easy conquest. Greco last month said M&A activity “is not really a priority” because the challenges and opportunities stemming from technological change can’t be addressed by combining businesses. “Consolidation doesn’t solve the issues,” Greco said in a Bloomberg TV interview. “The size of the company doesn’t really matter.”

Those views were echoed a few days later by Zurich’s Chief Risk Officer Alison Martin, who said big mergers are “incredibly distracting.”

Baete will also want to avoid the fate of his counterpart Thomas Buberl at Axa, whose shares have fallen about 12 percent since the XL acquisition was disclosed amid concern that he overpaid. His predecessors at Allianz also have a checkered record when it comes to M&A, underscored by the doomed 2001 purchase of Dresdner Bank AG.

In that context, the Allianz CEO’s comments to the FT may have been a signal to the broader market — and particularly to smaller insurers that are thinking of a sale — to view the German giant as a friendly suitor that’d be willing to treat the acquired business as an equal, offering autonomy in operations following a deal, the people said.

Even so, Allianz may face a tough road ahead in identifying the right target.

“In the case of XL, you had a willing seller and a willing buyer to pay the price,” UBS’s van Veen said. “As they get larger, it gets a bit more and more difficult.”