The Geneva-based bank said it was seeking charges against Pierre Condamin-Gerbier "for, among other things, theft, falsifying documents and violating professional and commercial confidentiality".
Condamin-Gerbier was earlier this month a witness before a French parliamentary commission investigating former budget minister Jérôme Cahuzac, who is facing charges of tax fraud.
The French minister resigned in disgrace in March over an undeclared foreign bank account said to contain around €600,000 ($770,000).
The former banker has told media he knew of 15 French politicians and "big names" with undeclared bank accounts in Switzerland and said he had handed the information over to French investigators.
According to news reports, he also provided detailed accounts of how Reyl helped rich French entrepreneur Alexandre Allard, who had been living abroad, to minimize his fortune of several hundreds of millions of dollars when he brought it back to France in a bid to dodge taxes.
"The numerous untruthful declarations given despite the bank's categorical denials, the falsification of an internal (bank) memo and its delivery to a French medium, has left the bank no other choice but to drop its reserve and act," Reyl said in a statement.
It said it had handed all evidence in the case to the Swiss public prosecutor's office.
The bank has repeatedly denied the allegations, and reiterated that it "has no bank account relations . . . with French residents who hold or have held political duties in France."
A Swiss daily, Tribune de Genève, meanwhile reported on that people "close to the family" of Condamin-Gerbier believed he may have been arrested in Switzerland upon his return after testifying in Paris on July 3rd.
An unnamed friend of the family told the paper the ex-banker had not been seen since July 4th.
"For the past week, we have not been able to contact him, which can only corroborate the thesis that he has been arrested," he said.
A spokesman for police in the southwestern Swiss canton of Vaud, where Condamin-Gerbier is believed to have been detained, told AFP he had no knowledge about the reported arrest.
His wife refused to comment on the arrest report, when contacted by AFP.