The Silicon Valley company is the world's largest advertising business, generating $60 billion a year from search, YouTube, and services such as Google Display Network and DoubleClick, which both deliver ads for third-party sites.
The executive at the mobile operator considering "the bomb" acknowledged that targeting Google could be risky from both a legal and public relations perspective. Under "net neutrality" rules in the European Union and the US, telecoms companies are forced to treat all data that flow through their networks equally.
But even within those markets, it would be feasible to block adverts on Google "just for an hour or a day" to bring the company to the negotiating table, the executive said.
More from the Financial Times:
Online arms race heats up over adverts
Screens collide in clash over advertising
Verizon looks to AOL for mobile ads edge
Many mobile operators are frustrated that digital media companies profit from their high-speed networks without having to invest in the infrastructure behind them. Such irritation was inflamed last month when Google launched Project Fi, its own wireless carrier in the US.
Google said it would be unreasonable for mobile operators to block ads, arguing that: "People pay for mobile internet packages so they can access the apps, video streaming, webmail and other services they love, many of which are funded by ads. Google and other web companies invest heavily in developing these services — and in the behind-the-scenes infrastructure to deliver them."
Blocking advertising on mobile networks is likely to provoke a fierce backlash from digital media companies. In 2013, Free, the French internet service provider owned by Iliad, blocked ads by default through its Freebox modem, causing huge controversy. It was forced to scrap the initiative within a week under pressure from the Socialist government.
Mr Carthy of Shine said that eliminating intrusive adverts is a "consumer right", even if it undermines the business model of online publishers that rely on advertising.
"Online advertising is out of control and it's polluting the user experience," he said. Pop-ups, auto-playing videos and other forms of digital advertising can consume between 10 and 50 per cent of a mobile subscriber's data plan, he added.
While ad-blocking is a new phenomenon on mobiles, it is more established on PCs and growing quickly. More than 140m people, or 5 per cent of the online population, use software such as Adblock Plus to eliminate adverts when browsing the web on laptops or desktop computers.
As the Financial Times reported in February, Google, Microsoft and Amazon have paid the makers of Adblock Plus to allow some ads on their sites to slip through its filters.
Google's relationship with ad-blocking is further complicated by the fact that such software is the most popular type of free add-on to Chrome, its popular web browser.