The classy forward has vowed to stay in Belgium until the end of the season but there is speculation a pre-contract could be agreed with the Merseysiders, who crashed out of the FA Cup on Wednesday at the hands of Championship strugglers Reading.
After being voted Belgian Player of the Year, the Serbian is rumoured to be in England discussing a potential transfer, says the News of the World.
Over Christmas, Jovanovic revealed: "I will be a Standard player until June.
"News that I have already said yes to AC Milan are not correct. I am still waiting, I haven't decided.
"I repeat - my options are still very open."