The Dutchman was rocked by the loss of several key attacking players during the summer transfer window, with the likes of Clint Dempsey, Mousa Dembele and Andy Johnson all seeking pastures new.
Arshavin, who has fallen from grace from at the Emirates Stadium, was linked with a switch to Craven Cottage during the summer. However, when asked whether he would launch a January bid for the Russian, Jol said: "No."
He was also pressed on reports he was tracking French starlet Vainqueur, to which he added: "I saw his name in the paper. That was probably the first [time I had heard it]. I Googled him afterwards."