Reds manager Brendan Rodgers is keen to add another marksman to his ranks before the September 1 transfer deadline, and the Colombian international fits the bill.
The Anfield side feel that the high-profile nature of Falcao would mark him out as an ideal replacement for Luis Suarez, who joined Barcelona last month for around £75m.
According to Radio RMC, Liverpool are ready to offer the Ligue 1 side £12m to allow them to take the striker on a short-term deal for the season, and the Anfield club are keen to insert a £31m release clause into any potential deal.
Liverpool have spent over £100m so far this summer, but have yet to add a new forward to their ranks since Suarez left for the La Liga giants.
A deal to land Queens Park Rangers striker Loic Remy for around £8.5m was cancelled at the 11th hour amid reports that the France international had failed his medical.