The demand, by a cross-party group of MEPs, comes after Barroso was recently appointed Chair and senior adviser at the international wing of the American investment bank Goldman Sachs.
Members of the parliamentary intergroup on integrity, transparency, corruption and organised crime (ITCO) said the appointment "damages the reputation of the European Commission and threatens the credibility of the EU."
They sent a letter to current commission head Jean-Claude Juncker, complaining about Barroso's move.
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The letter, seen by this website, says, "Barroso's appointment once again illustrates the necessity of a revision of the revolving-doors rules. Barroso has not infringed any of the Commission's revolving door rules such as the so-called 'cooling off' period, in which former EU Commissioners are not allowed to hold lobby positions, already passed.
"However, ITCO strongly believes that Barroso's move to Goldman Sachs, after presiding the Commission for two terms, during which important banking regulation was enacted by EU institutions, damages the reputation of the Commission and threatens the credibility of the EU as a whole among EU citizens."
In the letter, the MEPs urge Juncker to launch a legal procedure based on article 245 of the treaty of the functioning of the EU, which states that European Commissioners must "respect the obligations arising there from and in particular their duty to behave with integrity and discretion as regards the acceptance, after they have ceased to hold office, of certain appointments or benefits."
They point out that the same provision allows the Commission to apply to the European Court of Justice for the removal of Barroso's pension or other benefits.
The deputies stress "the importance" of revising the code of conduct for Commissioners in order to extend the cooling-off period from 18 months to 36 months.
They say, "We ask you to launch this legal procedure towards the removal of Barroso's pension/any other benefits and proceed with the revision of the code of conduct for Commissioners in order to extend the cooling-off period, within which former officials cannot take lobbying jobs, from 18 months 36 months.
"The extension of the period can ensure, in our view, that the ready access to EU officials, diplomats, and national leaders obtained by a former Commissioner would no longer be as relevant to the private sector trying to influence EU policies after five years."
The letter is signed by the group's co-Presidents, Dutch MEP Dennis de Jong, of the GUE group and Elly Schlein, an Italian Socialist, along with Portuguese S&D group deputy Ana Gomes, Irish ALDE group member Marian Harkin, Hungarian Greens MEP Benedek Jávor, Monica Macovei, a Romanian
ECR group deputy, Tomáš Zdechovský, an EPP group member from the Czech Republic and Italian Ignazio Corrao of the EFDD group.