Police investigating the case are also looking into trips made by the businessmen and a city police chief to Washington when Strauss-Kahn was head of the International Monetary Fund there, the Liberation and Le Figaro dailies said.
The last such trip ended on May 13 this year, the day before New York police arrested Strauss-Kahn for the alleged sexual assault of a hotel chambermaid.
Those charges were dropped after prosecutors deemed the alleged victim unreliable, although she is pursuing a civil case against the 62-year-old Socialist politician, who had been tipped as France's next president.
The French case began after the manager and the public relations chief of the Carlton hotel in the northern city of Lille were arrested and charged with arranging prostitutes for guests with the help of a pimp based in Belgium.
Lille police chief Jean-Christophe Lagarde, who was detained by police on Thursday for questioning as part of the pimping probe, allegedly attended evenings at a luxury Paris hotel along with prostitutes and Strauss-Kahn.
According to Le Figaro, David Roquet, head of a subsidiary of construction giant Eiffage, paid part of the tab from the Paris hotel sex soirees, billing his company with invoices marked with Strauss-Kahn's initials "DSK".
Police have also questioned another Lille businessman, identified as Fabrice P., who is also suspected of paying a part of the bill.
According to Roquet's testimony to police, cited by Le Figaro, "Fabrice P. told me that we would dine with Mr Strauss-Kahn and that he would like me to bring girlfriends, meaning prostitutes."
The first encounters took place at the L'Aventure club-restaurant in Paris in March 2009, where the men started having sex with the women before moving on to the luxury Morano hotel, he said.
Two other similar encounters allegedly took place in 2010. Relating one of the evenings, Roquet said he, Lagarde, Fabrice P. and Strauss-Kahn "went to a hotel, the Murano."
"We ate in the room and then we had paid-for sexual relations. We each had our girlfriend, I was with Jade, DSK also had his girlfriend and there were other people."
Roquet, who was on October 14 charged with pimping, said that Strauss-Kahn had not paid for anything. Eiffage on Friday said they had suspended Roquet with a view to dismissal, pending an investigation.
Roquet said that the group went to "visit the IMF" in Washington in May 2011 because "we were invited by DSK."
Asked who paid for the plane tickets, Roquet said: "I did, with the agreement of my boss. It cost me between 3,000 and 4,000 euros," Liberation quoted him as telling police, without elaborating on who the "boss" was.
Strauss-Kahn has told AFP that he wanted the authorities to question him as soon as possible over the allegations in order to end the "insinuations."
Police are investigating what the Lille businessmen and police chief might have gained in exchange for their apparent generosity, Le Figaro reported.