Mr Barroso headed the EU executive from 2004-2014 and will help the bank deal with the impact of Brexit. It is a powerful player in the City of London.
European Ombudsman Emily O'Reilly has written to Mr Barroso's EU successor, Jean-Claude Juncker, raising concerns.
The City is a key hub for EU business.
French politician Michel Barnier, the man who pushed through major EU reforms in financial services after the 2008 financial crash, will head the European Commission team in the Brexit negotiations.
Mr Barnier was financial services commissioner under Mr Barroso and some reforms, including caps on bankers' bonuses, met with British resistance.
The UK government is preparing for painstaking talks on the terms for withdrawing from the EU. There are fears that Brexit could harm the City's pre-eminent role in European finance.
Prime Minister Theresa May insists that "Brexit means Brexit" and is widely expected to trigger Article 50 - the withdrawal mechanism - next year.
Mr Barroso joined Goldman Sachs in July, in a highly controversial move. He respected the EU's mandatory 18-month cooling off period before moving.
Critics say it exposed once again a Brussels "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, signed by more than 62,000 people. The petitioners want Mr Barroso to lose his Commission pension.
Goldman Sachs donated hundreds of thousands of pounds to pro-EU campaigners, and said last month that Brexit could force it to restructure some of its business.
Ms O'Reilly told Mr Juncker: "Public unease will be exacerbated by the fact that Mr Barroso has publicly stated that he will be advising on the UK's decision to leave the EU.
"In this context, has the Commission considered issuing guidance to current Members, to Chief Negotiator Barnier and to staff in relation to how and whether they will engage with the former Commission President in his new role?
"Such advice is important given the need to ensure that their work is not affected by any possible failure on Mr Barroso's part to comply with his duty to act with integrity."
Ms O'Reilly investigates complaints about EU maladministration, and can order the release of documents, but cannot impose penalties.

Ramute Butkiene's remains were discovered after an unpleasant smell was reported coming from a room rented by boyfriend Vytautas Jokubauskas.
Jokubauskas, 57, of Mayor's Walk, Peterborough, was found guilty of her murder by a Southwark Crown Court jury.
Judge Nicholas Loraine Smith sentenced him to a minimum of 20 years in prison.
Jokubauskas, who had denied murder but admitted manslaughter, also pleaded guilty to preventing the burial of a corpse at an earlier hearing.
The torso of Ms Butkiene, 42, was found in the locked room on 5 June this year.
Jokubauskas had strangled Ms Butkiene with the cord from her dressing gown around a week ealier, the court heard, after accusing her of seeing another man.
He then dismembered her body before watching war films and drinking whisky with her torso stuffed into a suitcase next to him.
Jokubauskas buried her arms and legs in nearby wooded areas and disposed of her head before going on the run, jurors were told.
He was tracked down and arrested on 7 June, just a few streets away from where he had left his girlfriend's body.
During interview, he told police "I am a killer" and said he had strangled his girlfriend "just a little" to scare her.
Speaking after the sentence, Det Insp Pushpa Guild said: "This was a gruesome crime against an innocent woman, all because of a moment of jealousy.
"In a moment of rage, Jokubauskas killed Ramute and then butchered her in an attempt to cover his tracks."
A top EU official has questioned the European Commission's ethical standards over the new role of ex-Commission President Jose Manuel Barroso at US investment bank Goldman Sachs.
[NEXT_CONCEPT]
A "jealous" man who murdered his partner before dismembering her and stuffing her torso into a suitcase has been jailed for life.