It comes after the US Department of Health and Human Services said it had bought up 500,000 treatment courses, amounting to 100 per cent of Gilead's July production and 90 per cent for August and September.
Experts and campaigners condemned the move, saying it would hamper the efforts of countries across the globe to secure doses of the antiviral drug.
The EU Commission said it had taken note of developments in the US and is also talking to Gilead about its production capacity.
“Commissioner (Stella) Kyriakides has been in multiple discussions with the manufacturer, Gilead, including on their production capacity,” a spokesperson said on Wednesday.
“The Commission is also currently in negotiations with Gilead to reserve doses of remdesivir for EU member states.”
The US sparked outrage on Wednesday when it effectively stockpiled the entire world’s supply of remdesivir, which is exclusively manufactured by Gilead.
“They’ve got access to most of the drug supply [of remdesivir], so there’s nothing for Europe,” said Dr Andrew Hill, senior visiting research fellow at Liverpool University.
Remdesivir is only one of two drugs approved in the UK to treat the novel diseases, the other being dexamethasone – a cheap steroid found to reduce up to a third of deaths in patients with severe respiratory complications.
Remdesivir is an experimental antiviral drug first created and developed by the biopharmaceutical company Gilead Sciences in 2009.
It was originally created to treat hepatitis C but proved ineffective. Since then, it has been used to treat Ebola but did not work well against that disease.
Despite this, remdesivir later showed promise in fighting SARS and MERS — illnesses caused by coronaviruses — in animal studies and has been shown to reduce recovery times in seriously sick coronavirus patients.
The cost of remdesivir is around $3,200 (£2,500) per treatment of six doses, according to the US government.
After being approved for use in the UK at the end of May, health officials announced that remdesivir will be available to “selected NHS patients”.