Fifa is under investigation from the Swiss federal authorities over the cash for World Cup votes scandal, with the inquiry possibly leading to criminal charges, the Guardian can reveal.

Six senior Fifa officials, including an executive-committee member and vice-president, were last week suspended from all football activities for a total of 16 years after they were found guilty of corruption offences under the Fifa code of ethics. The director of Switzerland's Federal Office for Sport, Matthias Remund, wants to ensure that no Swiss laws have been broken.

Remund said the case would be analysed to determine "to what extent we have applicable law in Switzerland, in order to be able to pursue offences which are relevant from a criminal justice point of view or which offend competition law". The case is complicated since under Swiss law not-for-profit bodies cannot be pursued through anti-corruption laws, which apply only to commercial organisations. Remund said: "Private corruption in that [legal] sense does not exist in Switzerland. And in particular sporting associations and clubs without economic/commercial purpose are excluded from that purpose."

Whether or not the Swiss authorities pursue a criminal case, Fifa's exemption from anti-corruption legislation appears short-lived. Switzerland's sports minister, Uli Maurer, believes that in light of the most recent corruption case at Fifa House it is time to tighten that loophole and end its immunity from prosecution.

He said: "It's clear that Switzerland is obliged to do something to fight corruption as we have lots of international federations with headquarters in Switzerland and we want to set an example in solving this problem." In parallel with the investigation of the specific Fifa case, Maurer has tasked Remund's office with conducting a review of the anti-corruption laws to analyse whether these should also apply to sports organisations.

Fifa is ostensibly a not-for-profit organisation but the federal office is nevertheless focusing on the outcomes of its commercial activities. Fifa's own accounts prove it to be thoroughly profitable despite the fact it chooses to refer instead to the money it makes as a "surplus". Fifa's revenues in 2009 were $1,059m (£671m), in 2008 $957m, in 2007 $882m and in 2006 $749m. Over that four-year cycle Fifa's "surplus" amounted to $678m.

Fifa's president, Sepp Blatter, will run his campaign for re-election next year on a transparency ticket. "I told the members of the Congress I was going to run for office again because I want to be transparent," he said in June.