Riadh Ben Aissa, executive vice-president of the firm's construction arm, was fired in February along with Stephane Roy, the vice-president in charge of finances.
An independent review traced millions of dollars to the pair in payments to foreign agents for undocumented work between 2009 and 2011.
The Canadian Broadcasting Corporation, citing its Swiss counterpart RTS, said on Sunday that a joint probe by Canadian and Swiss police tracked money flowing from SNC-Lavalin to Swiss bank accounts registered to companies in the British Virgin Islands.
Some of the funds then went into Swiss bank accounts controlled by Ben Aissa.
Ben Aissa was previously linked to an elaborate plot to bring 38-year-old Saadi Kadhafi, the son of ex-dictator Moamer Kadhafi, into Mexico with false documents at the height of pro-democracy protests in Libya last year.
SNC-Lavalin oversaw billions of dollars worth of projects in Libya, including construction of a prison.
In April, the Royal Canadian Mounted Police raided SNC-Lavalin's Montreal headquarters as part of an investigation into the mysterious payments made through its office in Tunisia.