The 26-year-old Croatian international has netted 14 goals and six assists for the reigning SPL champions this season, and has attracted attention from a host of Barclays Premier League clubs.
Reds boss Kenny Dalglish has been credited with an interest in bringing Jelavic to Anfield this month, as he looks to add more firepower to his Liverpool frontline.
However, Blues boss Andre Villas-Boas could now rival the Merseysiders for his signature, after expressing his admiration for the talented forward.
"Jelavic is a great goalscorer," said Villas-Boas. "A player of his talent, with the right motivation at the right club, can continue to produce."
With Didier Drogba and Salomon Kalou away on African Cup of Nations duty this month, Chelsea are short on striker options themselves, with misfiring Fernando Torres, Daniel Sturridge and Romelu Lukaku the three available forwards at Stamford Bridge.
But the Portuguese tactician will face a fight to lure him to west London, after Jelavic recently admitted he was flattered to be linked with Liverpool.
"Of course it is nice to see your name being linked with that kind of club," he told Slobodna Dalmacija. "But I don't know if the rumour is true.
"Liverpool is a big club and anybody would like to play at Anfield but I'm just trying to stay focused on my game."