The Anfield outfit have offered the 28-year-old, who is out of contract in the summer, a three-year deal.
Liverpool manager Rafael Benitez has targeted the Serbia international as he looks to bolster his strike-force for next season.
Jovanovic is being tracked by a number of leading European clubs including Italian giants AC Milan.
Speaking earlier this month, the forward was non-committal over his future plans, and said: “News that I have already said yes to AC Milan is not correct. I am still waiting, I haven’t decided.
“AC Milan are not the only club interested in me. There is also Liverpool and another big European club. I repeat – my options are still very open.”
However, Liverpool are confident they have done enough to persuade Jovanovic to move to Anfield.
Jovanovic is a regular for the Serbia national team and is expected to play a major role for his country in this summer’s World Cup finals.