Rondon, who joined Rubin Kazan from Malaga just one year ago, has scored seven goals in 20 appearances for the Russian outfit.
And Liverpool boss Brendan Rodgers is desperate to add attacking reinforcements to his side as Luis Suarez looks likely to depart the Reds this summer.
However, now, the Champions League finalists have reportedly made contact with Kazan over the signature of the 23-year-old. Kazan are hoping to recruit the £8.7 million they paid for the youngster just last summer.
If Rodgers is to miss out on Rondon, he could turn his attention to Udinese forward Luis Muriel, who could be set to leave the Italian outfit.
Much will still depend on the Suarez situation as, so far, Liverpool have rejected bids for their star forward - despite the Uruguayan's intention to leave Anfield, as he goes in search of Champions League football.