Under the proposal, the EU Commission will disburse two-thirds of the funds in grants and the rest in loans to cushion the unprecedented slump expected this year.
The 500 billion euros in grants reflects the wishes of the two biggest EU economies, France and Germany, which came up with a grants-only proposal last week.
"In the event that we actually see the European Commission adopt a proposal in similar nature or stature of the France-Germany proposal, we do think that would be positive for the euro," said Parisha Saimbi, G10 FX strategist at BNP Paribas.
"We would expect to see euro/dollar head higher, and in particularly euro/Swiss head higher especially given the long positioning in Swiss (franc) has built up quite significantly and as a result you could see an exacerbated move to the upside as positions are covered," she said.
French Finance Minister Bruno Le Maire told France 2 television on Thursday that he hoped the European Union could reach a deal on the package in the coming weeks.
The euro was last flat at $1.1010, having risen earlier to a two-month high of $1.1035. The euro was up 0.1% versus the Swiss franc at 1.0670, though the day prior it rose to nearly a three-month high.
Leveraged hedge funds held $1.14 billion in Swiss franc long positions in the week to May 19, CFTC data shows, a near four-year high.
An index tracking the U.S. dollar against major currencies was stable at 98.93 as the greenback held its own in a crosscurrent between rising Sino-U.S. tensions and optimism over recovering global growth as economies re-open.
The war of words between the world's two biggest economies escalated, with Hong Kong the newest flashpoint, with U.S. Secretary of State Mike Pompeo saying on Wednesday that China's plan to impose laws there was "only the latest in a series of actions that fundamentally undermine" the former British colony's autonomy and freedoms.
The United States is currently crafting a range of options to punish China over its tightening grip on Hong Kong, including sanctions, tariffs and restrictions on Chinese companies, according to people familiar with the discussions.
The yuan was neutral at 7.1751 in the offshore market, though it remained close to the 7.1965 record low it sank to the day before.1 = 0.9076 euros)
(Reporting by Olga Cotaga; Editing by Kirsten Donovan) ((firstname.lastname@example.org))