Baroin's office said the minister had written to the European Union's current Danish presidency asking for examination of a draft law championed by President Nicolas Sarkozy to be examined by the summer.
The fact that nine countries are signatories to the letter is highly significant, as it paves the way for a special provision of the EU's Lisbon Treaty that allows at least one third of the EU's member states to trailblaze new laws by themselves.
This comes in the face of fierce opposition to an EU-wide tax from Britain, whose Prime Minister David Cameron said during the last EU summit that French banks would up and move to the City of London to escape the tax.
The so-called "enhanced cooperation" provision has already been used to overcome difficulties in harmonising some aspects of cross-border divorce law, and is also being used in moves to drive through a single EU patent despite decades-long objections.
The nine countries are: Austria, Belgium, Finland, France, Germany, Greece, Italy, Portugal and Spain.
The letter is signed by Italian Prime Minister Mario Monti and the finance ministers of the other eight, Baroin's office said.
In it, they say a tax is necessary "to ensure a fair contribution from the financial sector to the costs of the financial crisis, but also to improve the regulation of markets."
The nine are said to be giving their "full support" to a bid for EU governments to examine formal legislative proposals "in the first half of 2012."
President Nicolas Sarkozy announced last month that a French financial transactions tax would take effect in August, saying it would add one billion euros annually to state revenues.
According to a draft of the French legislation obtained by BFM Business and published on its website, the 0.1 percent tax will apply to acquisitions of shares belonging to "companies whose headquarters are located in France and whose market capitalisation exceeds one billion euros."