Earlier this month, Google was reported to have submitted a proposal to settle with the European Commission with regards to concerns expressed by the Commission’s head of competition, Joaquin Almunia. Details of Google’s proposal were not made public, but newer reports indicate that Almunia has added the condition that Google’s changes to its search results be applied to mobile search, as well as desktop.

This is according to a highly-cited Financial Times report (registration required), which indicates that Google could face a huge fine (in the billions), if Google and the Commission can’t reach an agreement. They’ve reportedly been negotiating since Google submitted its proposal at the beginning of the month.

The initial concerns laid out by Almunia, include Google’s displaying of links to its own vertical search services (as if Google’s competitors are playing the game so differently), Google “copying content from competing vertical search services and using it in its own offerings,” agreements between Google and partners on websites in which Google delivers ads, and “restrictions that Google puts to the portability of online search advertising campaigns” from AdWords to competitors’ platforms. You can see these concerns, as discussed by Almunia (verbatim), here.

It’s clear that the mobile approach to search is only gaining in importance as more and more consumers reach for their phones first, when looking to perform a quick search. Ironically, competition for Google is greater than it has ever been in the mobile space (see recent Apple announcements), and any restrictions set forth by government agencies will only hold Google back in the competitive landscape.

It will be interesting to see if longtime Googler, and now Yahoo CEO Marissa Mayer will be able to make any kind of mark for the struggling Internet giant. If I had to bet on any executive being able to turn search around for the company, Mayer would be on the short list of possibilities. If Google has its hands tied by government restrictions, it could be an opportune time for any such competitor to make significant moves. Yahoo has already been trying to make a bigger mark in mobile search with Axis. Mayer, no doubt, has plenty more ideas.

Microsoft obviously has plenty of its own ideas about mobile search, as Bing continues to gain market share, little by little.

Realistically, however, Google has already won over so many search users, who have been using Google for so long, it’s hard to imagine the company’s share of the market dropping too drastically (at least in the near term). User experience can go a long way, but brands and habits can be pretty hard to break.