John Schults/Reuters

Investors may not have much love for Facebook shares, but even the mere speculation that the social networking giant may buy a company can send a stock soaring.

That is what happened on Tuesday, when shares of Opera Software jumped by as much as 22 percent after reports surfaced that Facebook was looking to acquire the Norwegian Internet browser company.

By the end of trading in Oslo on Tuesday, the company’s shares were still up 19.5 percent, in the first day of trading since the reports emerged late last week.

On Friday, the British technology Web site Pocket-lint said Facebook was looking to acquire Opera to enter the Internet browser market. The deal, which would pit Facebook against the likes of Microsoft, Google and Apple, could give Facebook control over Opera’s highly-rated cellphone Web browser.

Opera, though, would not come cheap. In a research note to investors, the Norwegian bank DNB said Facebook or any other bidder might have to spend as much as $1.3 billion, or more than double Opera’s closing share price on Friday.

“The data harvested by Opera on its proxy-based mobile users, combined with the profile information Facebook has on its users, would make an appealing offering in terms of targeted mobile advertising,” the bank’s analysts said. “It could significantly help Facebook’s mobile monetization, which currently stands as a bit of an Achilles’ heel.”

Ahead of its much-anticipated debut, Facebook said it was facing challenges in reaching users through mobile advertising. The company, which raised $16 billion in its initial public offering, already has spent $1 billion in cash and stock on the popular photo-sharing application Instagram.

Opera could make an attractive target for a number of companies looking to expand in the fast-growing mobile Internet market. Google, for example, is in a good position to make a deal. It has close connections with the Norwegian company, as Google provides the search engine functions for Opera’s mobile Web browser.

A spokesman for Opera declined to comment on the speculation. A representative of Facebook was not immediately available for comment.