The Gabon international is a proven performer at the highest level, having found the target 139 times in 209 appearances for his current club – including a personal best 40-goal haul last season.
Those efforts have seen him register on the transfer radar of clubs across Europe, with La Liga giants Real Madrid reported to have been closely monitoring his situation at one stage.
Pressed on whether an approach could be made in the January window, new Toffees boss Sam Allardyce told reporters: "Possibly.
"It is the hardest thing to recruit today, a centre-forward who scores goals and is the right type of centre-forward who scores goals for you. That's the most expensive area on the pitch today.
"We've a number of players here who have reasonably good goalscoring records who haven't settled in - [Oumar] Niasse when he came from Russia, but has scored a few this year.
"And Sandro [Ramirez] who hasn't quite settled yet but scored lots of goals at Malaga last year.
"There are people who have scored goals here but if there's one out there that's ready and ready-made it would be 1) expensive and 2) you have to ask is it the right one?
"It's my opinion that my first signing has to be correct, has to be the right signing for Everton and for my future.
"Because if you make bad signings you get the sack. If you make good signings you become a better manager."
Everton spent big over the summer but have been unable to bring in a suitable successor to Romelu Lukaku following his £75 million move to Manchester United.
Aubameyang would help to fill those boots, but he will not come cheap either and the Toffees will need to see more funds made available if they are to address a problem area in their squad.