The EU is also concerned that the lack of transparency in China could mean new variants are not identified quick enough.
Brussels has offered to donate COVID-19 vaccines to Beijing in order to help it contain a mass outbreak of the illness following its decision to end strict nationwide restrictions.
The European Commission confirmed on Tuesday that the proposition was made in recent days by the EU delegation in China, but that it is yet to receive a response.
"In view of the COVID situation in China, Commissioner Kyriakides has reached out to Chinese counterparts to offer the EU's solidarity and support, including public health expertise as well as through variant-adapted EU vaccine donations," Commission spokesperson Tim McPhie told reporters in Brussels.
The EU is concerned that the lack of transparency in the country could mean new variants of COVID-19 are not identified quick enough.
Some countries have already implemented measures for travellers arriving from China, like mandatory negative tests. Italy, France and Spain will require this from passengers or proof of vaccination.
Beijing has described the restrictions as "unacceptable" and "discriminatory".
"We strongly oppose attempts to manipulate COVID measures for political purposes and will take countermeasures based on the principle of reciprocity," Foreign Ministry spokeswoman Mao Ning said.
But analysts say that for measures to be efficient, more coordination is needed.
A meeting of health experts and representatives of the 27 member states took place in Brussels on Tuesday.
One of the proposals they recommended is to monitor wastewater from planes coming from China to see if it yields new clues about any potentially dangerous variants - a measure already adopted by Belgium.
They also overwhelmingly came out in favour of pre-departure testing and backed genomic surveillance at airports and increased monitoring and sequencing.
"The reason why in Europe we propose to sequence all sort of variants that are derived from China is the relative transparency that China exhibits nowadays," Marc Van Ranst, Head of the Laboratory of Clinical and Epidemiological Virology at the Catholic University of Leuven told Euronews.
"They're not submitting really many sequences to the international databases...we are not sure that if a new variant would emerge that they would immediately put it into the database and that is pretty awful that we have to think that because we like to think that the Chinese colleagues are upstanding scientists, but at a certain moment in China, science becomes politics."
Van Ranst added that despite the focus being on China, more variants are emerging from the US.
Another meeting at the EU level, this time of the Council’s Integrated Political Crisis Response (IPCR), is scheduled for Wednesday.
Sweden's Minister for Social Affairs and Public Health Jakob Forssmed, who convened the meeting as his country now holds the rotating presidency of the Council, said in a statement, that "the Presidency is seeking a common EU approach to the possible introduction of entry requirements."
"It is important that we get the necessary measures in place quickly," he added.