The Financial Times said it had seen a letter from Malmström to Chinese commerce minister Gao Hucheng which contained the request.
The European Commission has been inundated by complaints from European producers, Malmström said in her letter. She urged the Chinese government, "in the wake of a worrying trend… to take all appropriate measures to curb steel overcapacity and other causes aggravating the situation", according to the Financial Times.
In her letter Malmström referenced the fact that the volume of Chinese exports of steel grew by more than 50% last year, and that price cuts to some products were "way beyond" any cut in the price of raw material or energy, the report said.
The European steel industry and unions issued a statement in November asking MEPs to create policies to bolster the European steel industry, saying that 5,000 jobs had been lost in the previous month. Since then, further job cuts have been announced by steel producers in the EU, including more than 1,000 jobs at Tata Steel plants.
Bart Samyn, deputy secretary general of IndustriAll union, has previously said that the layoffs are "the direct consequence of the regulatory burden at EU and member state levels, and in particular due to the dumping of Chinese steel on the EU market".
Chinese exports have grown to 110 million tonnes this year and doubled over the past two years. "The EU needs to do more to speed up the deployment of its trade defence instruments," IndustriAll said.