Ammann, already a double gold medal winner in the 2002 Winter Olympics, easily won the normal hill and is one of the favourites for this Saturday's large hill contest final.
"We request that the Swiss team stop using the new modified binding system immediately," a stern-faced Austrian ski jumping coach Alexander Pointner told a meeting of team captains.
"If not, a protest note will be submitted after the first competition round," he continued, saying the binding violated the rules and had not been tested.
Jumpers jump twice in Olympic competitions.
Earlier in the day Pointner told Reuters the modified binding allowed Ammann to increase his aerodynamic profile in the air and therefore soar further.
The Austrians, who have four of the five top jumpers in the world, came into the Olympics as one of the favourites. They performed poorly in the normal hill and were only able to win a bronze.
Swiss team captain Garry Furrer said the protest had more to do with the struggling Austrian team than the binding.
"We are using a binding we have already used in the World Cup ... we are sure our binding system meets the regulations," he told reporters after the meeting, saying it was unfortunate the Austrians had chosen not to respect Ammann's feats.
"It's more a problem for the Austrians than it is for us because we know we have a jumper who is really performing very, very well. They're getting nervous and that is not actually our problem," Furrer said.
Neither Ammann nor the four top Austrians took part in Thursday's official training session.
If the Austrians do protest on Saturday, a FIS jury will have to decide within half an hour whether it has merit.
If Ammann were disqualified from the large hill, Poland would then most probably point out that he had used the same binding for the normal hill and demand the gold be given to silver medallist Adam Malysz.
Pointner - stressing he did not want to overturn the result of the normal hill contest -- earlier said "we have to know what is legal and what is not legal".
He said his team had looked at the same binding modification in 2008 and had concluded it was too dangerous for its younger jumpers.
Austrian officials said they noticed the binding after the first day of training for the large hill on Tuesday, when Ammann jumped from a lower position than his rivals yet recorded the longest jump of the day.