The Tigers confirmed the news on their Twitter feed and said they would enter contract negotiations with Jelavic in the next few days.
After that game Roberto Martinez said: "I don't want to sell him - I don't want to lose him now, but I understand it is a key moment for him.
"Put it this way - if the World Cup was not in the summer, this situation would never be in place.
"It (any move) will not be a loan situation. That wouldn't allow us to replace Jela at all, so I don't think that would be right for us. It has to work for the player, but more importantly, for us as a squad.
"The only possibility would be a permanent move that would allow us to bring another striker in, so we are able to be as strong as we are with Jela."
Martinez's comments suggest heavily that Everton will look to bring in another striker before the end of the transfer window.
Chelsea loanee Romelu Lukaku has been their main striker all season with Arouna Koné having made little impact since signing from Martinez's old club Wigan in the summer.
The Croatia international joined the Toffees from Rangers in January 2012 for £5million and had an immediate impact, scoring 11 goals before the end of a season he finished as Everton's top scorer, despite arriving more than halfway through the campaign.
However, his form tailed off significantly in the second half of last season and he has struggled to break into Roberto Martinez's side following the arrival of Romelu Lukaku on loan from Chelsea, with Jelavic yet to score a league goal this season.
Jelavic, who was prolific for both Rapid Vienna and Rangers before moving to Goodison Park, has scored a total of 21 goals in 69 games for Everton.