The host country Canada wanted leaders of the G7 countries to discuss such a tax but dropped the idea after pressure from United States and Britain.
But the tax will be debated at a parallel meeting taking place only minutes away - The Other Economic Summit (Toes). This will be attended, not by leaders, but by representatives of pressure groups from around the world.
Nicholas Dunlop, who co-ordinates Earth Action, a London-based network of more than 1,000 groups, believes that as the G7 discusses ways of strengthening international financial institutions, it should tackle currency speculation by means of a tax, with the money raised being used for "sustainable development in the poorest nations".
Nobel Prize-winning economist James Tobin has suggested a tax of 0.05 per cent on all international currency transfers. The primary objective of the tax would be to discourage speculative runs on key world currencies, which Mr Tobin believes are damaging the real economy. The tax would also give national governments more autonomy to set interest rates at a level appropriate for their own country.
An estimated $1,000bn (pounds 625bn) crosses national borders every working day. A tax of 0.05 per cent on all transactions would raise about $150bn a year. This is nearly three times the level of current development aid. Mr Tobin proposes that the tax be paid into a central fund.
Canada's Prime Minister Jean Chretien says that the G7 countries and institutions such as the IMF have concluded that the Tobin tax "could impede international financial flows". Critics are likely to focus on how the tax might deter legitimate foreign trade.
But Mr Jacob von Uxehull, one of the co-ordinators of Toes, believes that currency speculation would be curbed by the tax.
At the Toes meeting this week, Sir Shridath (Sonny) Ramphal, the former secretary-general of the Commonwealth, will present the conclusions of the commission on global governance, which he has co-chaired with Swedish Prime Minister, Ingvar Carlsson. This will endorse the idea of a Tobin- style tax. Toes intends to press leaders to think about the issue again.
At the Copenhagen social summit in March, former French President Francois Mitterand strongly supported the idea of a tax on currency speculation. Its chances this week could depend on whether Jacques Chirac now picks up the idea.