Tajani, now an MEP, has already appeared before the committee to explain his role, as former Commissioner for industry and entrepreneurship, in the scandal.
On Wednesday, Greens/EFA group MEP Bas Eickhout said his group are likely to demand that Tajani is recalled to give evidence to the committee because of "dissatisfaction" at his earlier appearance.
Eickhout said, "Tajani's only line of defence seemed to be that 'I did a great job'.
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"But, in a 90 minute appearance before the committee, he did not give satisfactory answers to questioning by MEPs. There was general dissatisfaction with his performance and it is for that reason that we are likely to insist that he is recalled. What we are saying to Tajani is this: You are not off the hook."
The committee of inquiry into emission measurements in the automotive sector (EMIS) is currently considering the EU response to the Volkswagen emissions scandal.
While rules on car safety and environmental standards are agreed at an EU level, implementation of car certification, called type approval, is done at national level.
The Volkswagen scandal was revealed following a study into differences between emissions from diesel vehicles in the US and Europe.
Last September, the German car manufacturer admitted to fitting cheat devices to more than 11 million vehicles. These were designed to deceive US authorities on the levels of harmful nitrogen oxide (NOx) emitted by a popular range of its diesel engines.
The firm agreed to recall affected vehicles and remove the cheat devices.
Parliamentary inquiries and criminal investigations were launched in several jurisdictions, including the European Parliament which set up the special committee of inquiry.
Another former Commissioner, Janez Potočnik, who was in charge of the environment dossier from 2010 to 2014, recently attacked VW for its "irresponsibility" over the scandal.
Eickhout dismissed suggestions that the committee was a "cosmetic" exercise, insisting that the aim was to "push governments" to ensure there was no repeat of dieselgate.
He said, "Of course, the conclusions and recommendations that are eventually made will not be legally binding so whether it leads to better legislation at national level remains to be seen."
On Thursday, German transport minister Alexander Dobrindt will appear before the committee, the first national government minister to do so.
Greens co leader Rebecca Harms said she "welcomed" the decision by Dobrindt to speak to the committee, saying, "This is a good opportunity to ask some key questions including his curious position regarding Fiat. He seems to think it is ok for defeat devices to be used in Germany but banned in Italy."
Speaking at the same briefing, French Greens MEP Karima Delli criticised France's environment minister Segolène Royal for appearing to be reluctant to appear at the committee.
Delli said Royal had agreed to give evidence, during the Strasbourg plenary in November, only after coming "under pressure."
"This is an important inquiry, doing serious work but she was very reluctant to come. This sort of response is not acceptable," she said.
Delli said the committee had already produced results and cited, as an example, the pledge by the Commission to take infringement proceedings against member states that do not comply with new emissions rules.