The watchdog is looking into the firm which Shapps used to sell advice on how to make money from the internet using the pseudonym Michael Green.
Sky News spoke to friends of Mr Shapps who said they believed the complaint to be politically motivated. They emphasised he has sold his share in the company and has not had any dealings with the firm since 2008.
The complaint comes days before the Conservative Party conference is about to start in Brighton.
Labour MP Steve McCabe said Mr Shapps had "multiple personalities and questionable business practices" while Lord Prescott dubbed him "two tags" - a reference to his own nickname of "two Jags".
But Paul Staines, the influential political blogger Guido Fawkes, said on his site: "The internet guru won’t be breaking a sweat just yet – as Guido understands it there were no paid adverts on websites run by the Tory chairman’s alter ego so there is no advert to ban. In any case the ASA has no statutory authority, no mandate and no enforcement powers.
"It’s hardly surprising that they would get involved though. The ASA is chaired by Chris Smith, the former Labour MP and now peer. They are a censorious bunch of self-appointed bureaucrats making politically correct judgements in areas they should not go into. To call them a “kangaroo court” would be to insult the powers of jurisprudence wielded by antipodean mammals. They have no place in a free democracy."
Speaking to Sky News last weekend Mr Shapps said: "Before I went into parliament I used to write business publications, and like many authors wrote under a business name.
"I was always very open about it and I actually went to one conference, where that picture was from, it was sort of an open fact. It was in my biography, it was in the conference programme.
"I have seen some extraordinary headlines though, things about living double lives as though I was François Mitterrand with his second family and things.
"My wife and I set up the business, we were always very open about it and had a business author's name as many authors do. It was all a long time ago, I've not been involved for a long time."
The news of an investigation into this complaint follows reports in The Guardian in September that the software package TrafficPaymaster, founded by Shapps, and now run by his wife Belinda, created web pages by "spinning and scraping" content from other sites to attract advertising from Google.
But the paper claimed this method breacheed Google’s strict code of practice on unoriginal content.
