They quote judicial sources as saying that Paris appeals court will now study a request by Mr Sarkozy for the case to be dismissed.
Mr Sarkozy, 59, is still facing several other judicial investigations.
Last week he said he would seek the leadership of the opposition UMP party - the move widely seen as a first step towards a presidential bid in 2017.
His announcement ended months of speculation about the intentions of the conservative former president, who vowed to give up politics after he failed to be re-elected in 2012.
The UMP party elections are due to be held in November.
Although Mr Sarkozy has kept a low profile since leaving office, he has faced a series of investigations that involve him in some capacity.
The suspended case relates to an alleged attempt to influence judges who were looking into his affairs.
The suspension could last several months, according to AFP news agency.
Other inquiries include one into his links with late Libyan leader Col Muammar Gaddafi and another into illegal campaign funding in 2012.
Mr Sarkozy denies wrongdoing.
A corruption investigation against French former President Nicolas Sarkozy has been suspended, French media say.