The Portsmouth midfielder raised the roof of Villa Parkwhen his two long range goals led to the 3-1 defeat of home side Aston Villa on Saturday.
His performance won him the player-of-the-week with both goals competing for the Goal of the Season award.
Essien, who has been Ghana's top player in the past two seasons in England, looks to have stiff competition on his hands after Muntari's showing on Saturday.
Muntari is a close friend of Essien but he is confident he can be Ghana top scorer in the Premiership this season thanks to the four goals he has scored so far.
"Maybe I will end up with more goals than Essien," Muntari said.
"I wouyld also like us to break into the top fouyr and if we keep playing this way I can't see why we can't do it."
Muntari joined Portsmouth in the summer from Italian outfit Udinese for a club record fee of US$14m.