The Monaco forward is rumoured to be ready to end his time on the Mediterranean coast after just one season, and has been linked with a loan move to Anfield.
With Luis Suarez sold and Daniel Sturridge short of back-up, Brendan Rodgers is desperate to cap his mega summer of transfer action by landing a top goal-getter.
And even though Falcao has his heart set on Real Madrid – whom are interested – Liverpool are still in the hunt for the Colombian.
Rodgers’ side have been buoyed by the fact Real Madrid cannot afford another big deal just yet after spending almost £100m in recent months, which could give them an advantage.
Although a loan move has been mooted, Monaco are keen on a full sale if they are forced into letting their hit-man go, which Liverpool can afford due to the big cash injection brought in by Suarez’s exit.