Self was responding to a Reuters report that the European Commission has asked Luxembourg for information on the tax arrangements it has put in place for McDonald's.
Reuters said that a source had told it that unnamed trade unions from the US and Europe and UK-based charity War on Want have asked the Commission to look into McDonald's tax affairs between 2009 and 2013.
"The Commission has sent a letter to Luxembourg asking them to clarify the facts," the source told Reuters.
Self said: "It is clear that there is increasing pressure on the tax affairs of US multinationals in particular – not only from the EU, but also from new measures such as the UK Diverted Profits Tax and similar measures which have been proposed in Australia. Companies should now be reviewing their tax position, in response.”
A spokesman for competition commissioner Margrethe Vestager told Reuters: "Combating tax evasion and avoidance is a top priority. The Commission is taking a structured approach when using its state aid enforcement powers to investigate where it believes that selective tax advantages distort fair competition."
Competition expert Caroline Ramsay of Pinsent Masons, the law firm behind Out-Law.com, said: "It is clear that the European Commission’s interest in state aid and taxation is not waning. Luxembourg is still very much a member state of interest in relation to its approach to tax rulings but other European member states are not being ignored."
"The European Commission announced in December 2014 that it would extend its tax ruling probe to all 28 member states and, in February this year, the Commission announced it was investigating Belgium’s tax regime which allows companies to reduce their tax liability on the basis of excess profit," she said.
In January, the European Commission said that corporation tax arrangements agreed between Luxembourg and the online retailer Amazon in 2003 may have conferred a "selective tax advantage" on Amazon.
The Commission recently unveiled new proposals to help identify corporate tax avoidance by sharing more information between member states.