Toronto, who were promoted last month, are close to confirming the signing of Williams on a lucrative two-year contract.
The Daily Telegraph revealed that Brian McDermott, Toronto's head coach, watched the 34-year-old play for the All Blacks in their World Cup semi-final defeat by England in Yokohama, in which Tuilagi played.
They later held face-to-face talks and, as reported by The Telegraph on Saturday, Williams has been offered a deal that includes a minority stake in the Canadian club.
Now the club want to sign Tuilagi to further bolster their ambition to become a global sporting brand.
The 28-year-old Leicester centre turned down a big-money move to French club Racing 92 this year and signed a contract extension to keep him at Welford Road until June 2021. Ben Te'o, the Toulon centre, who won 18 England caps under Eddie Jones, also remains on Toronto's radar. It is believed Toronto have had contact with representatives of both players.
The Wolfpack would be required to pay a sizeable fee to sign Tuilagi, but the acquisition of Williams in a sports-mad city has set the pulses racing on both sides of the world.
One source told The Telegraph: "A lot of NRL players are now cold-calling Brian Noble, Toronto's director of rugby, about joining.
"The signing of Sonny Bill shows how serious the Wolfpack are in trying to crack the North American market. They want to sign players who are considered 'rock stars' in order to change the face of Super League. Manu Tuilagi is definitely next on their list."
Significantly, new rules were introduced two years ago to allow Super League clubs with sufficient funds to bring in players from outside rugby league without it affecting the wage cap.
The Wolfpack are unable to play at the Lamport Stadium until April because of the harsh Canadian winter and the unavailability of their local authority-owned stadium, so have switched their first three home fixtures. They open against Castleford in a double-header at Headingley on Feb 2 and play champions St Helens at Allianz Park, home of Saracens, on Feb 29.