Sending Italy and France, the second and third-biggest eurozone economies, back to the drawing board would be unprecedented for the EU and potentially explosive politically.
In addition to the two heavyweights, Austria, Slovenia, Malta and Finland have also been notified by the European Commission that their budgets for 2015 could be in serious violation of spending rules, the source said.
European Commission spokesman Simon O'Connor confirmed that some countries had been notified but refused to name them.
However O'Connor insisted that any notification by the Commission to member states "does not prejudge the outcome of our assessment."
Last week EU member states which use the euro currency submitted their spending plans for next year 2015 to the Commission, the EU's executive branch, in accordance with vast new powers of oversight handed Brussels at the height of the eurozone debt crisis.
Under these new procedures, the Commission had until Wednesday to notify member states with accounts which raised questions, and a week after that to decide whether these countries were in "serious" breach of the rules. Brussels officials would then have the the power to demand changes to the budgets.
Italy is under the EU microscope, with Italian Prime Minister Matteo Renzi walking a tightrope between defending France - and its seeming defiance of Brussels over cutting its deficit - and keeping in the good graces of the Commission.
With next week's deadline nearing however, expectations are growing that sanctioning Italy and France directly would be a step too far, even for Germany, the EU's most powerful member state and a defender of sound public finances.
Last week, a report in Der Spiegel newspaper said Germany was helping France to draw up a pact with the European Commission on deficit reduction and structural reforms to win Brussels' approval of its budget.
While the report was never confirmed, the French and German economy ministers on Monday showed a united front at a mini-summit on investment in Berlin.