Anyone puzzled by the sudden jump in Twitter’s share price this week could have usefully checked out stock market news site briefing.com. The social network had hired Goldman Sachs, the investment bankers, the site claimed, to defend itself against being snapped up by Google.

The trouble was this was at least the third time the two have been linked. The same rumour had surfaced as recently as January and dates back to at least February 2011, before the micro-blogging site went public. The company declined to comment on the claims either time; neither responded to a request for comment this time.

Nevertheless, if a deal were to happen, it would be the second-biggest ever acquisition in technology, well ahead of Facebook’s $19bn (£13bn) purchase of WhatsApp in 2013 and behind only the $106bn AOL-Time Warner merger of January 2000.

Twitter is valued at about $33bn. Google has around $60bn in the bank, though a lot of that is stashed overseas to avoid taxes on repatriation; a share- or debt-funded acquisition might be simpler.

But why would Google be interested in Twitter?

The short answer is that Twitter, whose users send out 140-character “tweets” visible to anyone who follows them, has something the search and data specialist does not: a thriving, engaged social network.

Despite multiple attempts by Google down the years to build something similar, it can only look on in envy at Twitter’s 300 million users logging on every month, sending over 500m tweets every day on the topics that interest huge swathes of the world.

Eric Schmidt, Google’s chairman (and chief executive through its fast-growth years), told Bloomberg in December that “the biggest mistake that I made was not anticipating the rise of the social networking phenomenon”.

He added: “It’s not a mistake we’re going to make again. In our defence, we were working on many other things, but we should have been in that area, and I take responsibility for that.”

Some think Google’s problem with “social” is that its data-driven culture tends to be blind to the tweaks that make people love social networks. But as mobile use becomes dominant, social networks offer the most valuable advertising space. In the fourth quarter of 2014, 69% of Facebook’s advertising revenue came from mobile ads, up from 53% a year before; and revenues were up 49%.

Google, by contrast, has seen its cost-per-click (what advertisers pay when someone clicks on an ad) decline by 30% over the past four years as mobile use has grown, limiting its potential for revenue growth. Google, of course, relies on advertising for 90% of its revenues, and perhaps more of its income.

Ben Thompson, an independent technology analyst who writes the Stratechery blog, said the contrast with Facebook shows Google “is behind both on mobile … and potentially in brand advertising, which works best in a ‘stream’. Twitter is a route back to both.”

It’s not that Google hasn’t tried. The search company has targeted “social” at least four times since January 2004, when it launched the first, a Facebook-like social network called Orkut. That became hugely popular in a number of countries, including Brazil and India. But Facebook outpaced it, and was focused where Google wasn’t; Orkut finally closed down in September 2014. It tried with Jaiku, a Twitter-like service acquired in October 2007, which it effectively abandoned in 2009 and shut in January 2012.

It then tried again with Buzz, started in February 2010, creating a “social network” based on your email recipient database. That was calamitous: complaints that it violated its own privacy promises led to quick action by the US’s Federal Trade Commission, which in March 2011 bound Google over for 20 years to “regular, independent privacy audits”. Buzz was shut down in October 2012 – though the privacy audits remain in force.

Most recently Google+, launched in June 2011, tried to add more precision to Facebook’s simple idea of “friends” by letting you create “circles” – such as family, friends, colleagues and special interest groups – with whom you could share different content.

Yet despite being bolted on by default to every Google Mail account – and so rapidly rising to hundreds of millions of users – Google+ has never gained traction. Facebook was already too big, and people found it too taxing sorting their contacts into different circles, and then having to decide what was appropriate for each of them to see when sharing content. Its biggest success has been as a photo repository because of the automatic upload from Android phones; keen photographers love it.

While Google+ has not been widely popular, it has been effective at doing what Google wants – gathering information about peoples’ web activity and visits (because once you had logged in, it could follow your online movements). It has now been uncoupled from Google Mail, but its purpose remains.

Vacuuming up all that data about peoples’ online habits would only get easier through Twitter. In an interview with the Guardian in 2009, Marissa Mayer – then still at Google as head of search – enthused about “real-time search”, which is what Twitter in effect offers. For example, she said: “You can ask: ‘Is this conference today any good? Is it warmer in San Francisco than it is in Silicon Valley?’ You can actually look at tweets and see those sorts of patterns, so there’s a lot of useful information about real time and your actions that we think will ultimately reinvent search.”

Technology analyst Jan Dawson, who runs Jackdaw Research in Utah, said: “If Google could provide integration between Google and Twitter accounts, it could suddenly do ad targeting a lot better than Twitter is currently able to do, which could boost both sides of the business.”

But, he points out, “to really get the benefits of integration, Google would need to connect Google and Twitter IDs, and the last time Google undertook a big ID integration effort it got hammered by regulators across Europe”. (Google is threatened with fines by privacy regulators in Europe over its integration in January 2012 of separate user IDs from search, YouTube and other Google properties.)

Dawson said: “Google’s problem in social is less a cultural handicap and more just that it’s really tough because success relies on quickly gaining critical mass which generates positive network effects. It’s hard for anybody, as confirmed by the fact that only two social networks have really taken off on a global scale, and one is utterly dominant. Buying the smaller of the two major global social networks is arguably the most feasible way to get into the business at this point, so it makes sense for that reason.”

However, Thompson thinks the acquisition is “very unlikely, primarily because I’m not sure it makes sense at the price Twitter would command.

“That aside,” he adds, “I do think it would be great for both companies.”

Dawson agrees: “I could see Twitter’s management resisting it because they finally have their strategy in place and are starting to execute on it. If I were them, I think I’d rather follow through on that than see someone new take over.”

What Google could bring to Twitter:

1) huge number of advertisers already using Google AdWords and AdSense

2) global reach

3) potential inclusion by default in Android mobile software

4) integration with YouTube for short and long video

5) resilient systems

What Twitter could bring to Google:

1) highly engaged social network

2) users’ instant “sentiment data”

3) different dimension to “search”

4) mobile-optimised platform for advertising

5) positive reputation on privacy