Barroso headed the Commission from 2004-2014 and will help the bank, a powerful player in the City of London, deal with the impact of Brexit.
But ombudsman Emily O'Reilly said his move has sparked concern "at a very challenging time for the EU and particularly in relation to citizen trust in its institutions."
Her concerns are highlighted in a letter to Commission President Jean-Claude Juncker.
O'Reilly investigates complaints about EU maladministration, and can order the release of documents, but cannot impose penalties.
The Irish-born official said that "this is a significant public interest issue and must be openly and comprehensively addressed."
O'Reilly said "public unease will be exacerbated by the fact that Barroso has publicly stated that he will be advising on the UK' s decision to leave the EU."
The Commission's Brexit team is led by French politician Michel Barnier, who was Commissioner for internal markets and services during Barroso's second five-year term. O'Reilly wants to know whether Barnier and other staff have received orders on how to "engage" with Barroso.
Barroso joined Goldman Sachs in July, in a highly controversial move. He respected the EU's mandatory 18-month cooling off period before moving but critics say it exposed once again a "revolving door", in which elite EU officials move to lucrative jobs in business, deploying their inside knowledge and expertise.
Transparency campaigners have launched an online petition so far signed by more than 62,000 people. The petitioners want Barroso to lose his lucrative Commission pension.
Goldman Sachs is particularly toxic for some, as the bank has been accused of misleading investors about the quality of its loans ahead of the 2008 financial crisis. Goldman is also alleged to have helped the Greek government hide details about its national debt for more than a decade.
In July, Juncker told French media that "the fact that the former President works for a bank does not pose a problem. But for that one, that one poses a problem for me. You must carefully choose your employer."