Steve Bruce has been looking to boost his forward line in the January transfer window and has been linked with the two players for some time.
Croatia international Jelavic moved to Goodison Park from Rangers in a £5.5m deal two years ago but has struggled to earn a regular starting berth under Roberto Martinez this season.
Jelavic has made only 10 Premier League appearances this season though and scored his first goals of the season in the 4-0 FA Cup win over QPR.
But Bruce is understood to have made the 28-year-old his top transfer target for the January window and he looks to have got his man.
"He will sign today," Allam said of Jelavic when interviewed by Sky Sports News.
"It's a massive deal, our biggest ever. The club is moving forward."
Allam is also hopeful they will also be able to bring Republic of Ireland international Long to the KC Stadium.
Long has been linked with a move to East Yorkshire for some time, although Bruce was forced to issue an apology last week after media reports claimed they had already agreed a deal with West Brom for the player.
Allam is hopeful the move will be completed though, leaving Bruce with a potentially new strikeforce for Saturday's trip to Norwich.
"I hope so. I think we agreed terms," said Allam when asked about Long.
"It's a matter of talking, getting the club to release and the player to agree."