The EU's competition commissioner has indicated she is ready to look into complaints about the £130 million tax deal struck between HM Revenue & Customs and Google.
The Scottish National Party has written to commissioner Margrethe Vestager, calling on her to investigate whether the settlement, covering the past 10 years, breached EU rules.
Ms Vestager said it was "too early" to say if a probe would be launched into whether the deal amounted to "illegal state aid", but Labour MP Margaret Hodge - former chairwoman of the Commons Public Accounts Committee (PAC) - said she should "take a look".
Executives from Google and HMRC bosses are to be grilled on the deal by the PAC on February 11 in the latest of a series of probes by the influential spending watchdog into multinationals' tax affairs.
The internet search giantd efended the controversial deal, insisting it had complied with the law and was paying "the full amount of tax that HM Revenue & Customs agrees we should pay".
But one of the tech company's biggest UK shareholders said it should pay "much more".
James Anderson - whose Scottish Mortgage Investment Trust owns £120 million of shares in Google's parent company, Alphabet - told The Times: "It is in the long-term interests of Google and others of that ilk to pay decent rates of tax ... They are beneficiaries of state spending at many levels and in return they would get respect."
The deal also came under fire from News Corporation chairman Rupert Murdoch, who tweeted that the company was "paying token amounts for PR purposes" and should "pay like the rest of us".
The settlement was initially hailed as a "victory" by Chancellor George Osborne, but Labour said the amounts recouped were "trivial" and leader Jeremy Corbyn told the House of Commons that experts had estimated it meant the company was paying at a rate of just 3% - a figure disputed by David Cameron at Prime Minister's Questions.
In a letter to Ms Verstager, SNP economy spokesman Stewart Hosie wrote: "Considering the lack of transparency in the settlement reached between HMRC and Google, and the growing concerns of an opaque methodology having been employed, it is my view that an independent verification of this settlement would establish confidence that the settlement is within the boundaries of state aid regulations and is a fair deal for the taxpayers of the United Kingdom."
Mr Hosie said there was "a palpable sense of scepticism" among the public and experts about the settlement, adding: "Working people and small and medium businesses do not have the luxury of negotiating down the amount of tax they have to pay - and we must now have independent verification that Google has not been extended that luxury by this Government."
Asked whether she would launch an investigation, the competition commissioner told the BBC Radio 4 Today programme: "That is way too early to say because I don't know the details of the deal.
"If we find there is something to be concerned about, if someone writes to us and says this is maybe not as it should be, then we will take a look."
Ms Verstager said that so-called "sweetheart deals" for big companies were "unfair" and could amount to illegal state aid.
Lady Hodge told Today it was time for big companies listed on the Stock Exchange to "open up these negotiations that they have with HMRC ... so you see the assets, you see the business that takes place here in the UK, we see the profits they make and then we can all judge that they pay a fair rate of tax".
In a letter to the Financial Times, Google's vice president of communications and public affairs, Peter Barron, insisted the company paid UK corporation taxes at the standard rate of 20%.
Mr Barron wrote: "As a US company, we pay the bulk of our corporate tax in the US: 3.3 billion dollars in the last reported year. What should Google pay in the UK? We pay tax based on the value added by the economic activity of our staff here, at the current standard rate: 20%.
"After a six-year audit we are paying the full amount of tax that HM Revenue & Customs agrees we should pay, including £130 million in additional back tax.
"Governments make tax law, the tax authorities independently enforce the law, and Google complies with the law."