London currently processes three-quarters of the trade in this financial sector, providing thousands of jobs.
But European Commission vice-president Valdis Dombrovskis said Brexit needed "certain adjustments to our rules".
The law will decide if London will have the right to host the work post-Brexit.
London is currently the world leader for the clearing of all types of currency-denominated derivatives including the euro.
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Clearing is the process by which a third party organisation acts as the middleman for both buyer and seller of financial contracts tied to the underlying value of a share, index, currency or bond.
Trillions of euros are handled through clearing houses every year, mostly through London.
In a statement, Mr Dombrovskis said: "As we face the departure of the largest EU financial centre, we need to make certain adjustments to our rules to ensure that our efforts remain on track."
The financial industry has warned that forced "relocation" of the work would split markets, increase trading costs, weaken the euro and threaten the jobs associated with the clearing houses in London.
The proposal would split clearing houses into two tiers, determined by whether their operations are considered to be "systemically important".
If they are not thought to be important, then they will carry on working under the structure of the European Market Infrastructure Regulation.
More important "tier two" institutions will have to meet extra requirements set by EU central banks, could face "on-site inspections" and will have to give "all relevant information" to the European Securities and Markets Authority.
Those requirements may not be enough for the clearing houses thought to be the most important, which would force their operations back inside the EU.
A move like that could affect the clearing house at the London Stock Exchange.
The proposals will now go before the European Parliament and the European Union Council.
The policy chairman at the City of London Corporation Catherine McGuinness said "fragmentation" of foreign exchange and interest rate trading could see firms' costs increasing by "as much as 20%".
She said the Corporation was also concerned that it could "increase systemic risk".
"The UK is the only place that can guarantee financial stability with the lowest possible cost implications," she added.
Meanwhile, the UK Treasury said: "How UK firms access EU markets, and vice versa, is a matter for the forthcoming exit negotiations.
"In the meantime we stand ready to engage constructively on this legislation."
Source: BBC News