Draft documents seen by The Financial Times show the European People's Party (EPP) and the European Socialists & Democrats (S&D), the largest parties by seats in the European Parliament with more than half the votes, backing a motion that calls for the search giant to split up.
"Unbundling [of] search engines from other commercial services" could appease those concerned by Google's dominance in the European market, the publication cited the motion as saying.
The draft motion is the most far-reaching of all proposals to date.
Although the motion, if passed, would not force Google to split up, it would pressure the European Commission, which is accountable to the European Parliament, to seek resolution from Google.
Failing that, Google could be barred from operating certain services in the region.
The European Commission declined to comment.
Google, which has about 90 percent of the search market share in the European Union, has come under heavy fire from European parliamentarians and regulators alike for its alleged business practices.
Those allegations, detailed in a May 2012 letter to Google chairman Eric Schmidt, include copying content from competing search engines, and restricting the portability of data out of its advertising platform to competing services.
The leak of the draft motion comes less than two weeks after Europe's new antitrust and competition commissioner, Margrethe Vestager, said it would take time to consider the next step in the ongoing probe.
The probe as it stands is currently in hiatus as Vestager evaluates the European Commission's next move.
"The issues at stake in our investigations have a big potential impact on many players; they are multifaceted and complex. I will therefore need some time to decide on the next steps," Vestager told members of the European Parliament in a hearing in Brussels.
Despite three rounds of concessions, her predecessor Joaquin Almunia ultimately rejected the third and final offer, leaving Vestager to handle the Mountain View, Calif.-based technology giant.
Should Google be found in breach of Europe's antitrust or competition rules, it could be fined up to 10 percent of its global revenue for the infringing years.
A vote in the European Parliament is expected on Thursday, according to the FT.