They are concerned EU countries might have to pick up the tab if anything goes wrong with the vaccines.
ADVERTISEMENTMEPs have called for transparency over the terms of the European Commission's coronavirus vaccine contracts.
They want to know what is written into the contracts signed with pharmaceutical companies and who will be responsible if anything goes wrong.
"The commission tells us that there haven't been changes in the legal rules of the game," said French MEP Pascal Canfin.
"And I have no reason not to believe it. But if this is the case, then they should make public the articles of the contract related to this issue because this would give certainty to everyone and it would also silence all the rumours that say the laboratories are rushing things through and therefore want to be exempt from any legal responsibility if there are problems with or side effects from any vaccine."
Pharmaceutical companies have been pushing for exemption clauses, so, in the case of any problems, member states would have to pay some of the compensation.
But some experts fear that the lack of transparency could lead to a lack of trust among citizens.
And there is already an alarming number of people who don't want to receive any vaccine if and when one becomes available.
"I am convinced that transparency and being pro-actively transparent [and] straightforward with citizens is the only way forward, it is the only way to counter 'anti-vacciners' [and] conspiracy theories," Yannis Natsis from the European Public Health Alliance told Euronews.
"It is the only way to ensure or to increase the chances of having a successful deployment of this product, of these vaccines."
The EU's health commissioner insists that safety is of the highest priority but also defends the need for secrecy as negotiations with other pharmaceutical companies continue.