The Gabon global 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.
Aubameyang is reportedly available for £60 million, and Everton's interest has reportedly been captured.
Allardyce has spoken of the need to significantly bolster his lopsided first-team squad when the January window opens, and the 63-year-old is eyeing strikers and defenders to provide competition for places in those areas.
"It's the hardest thing to recruit: a centre-forward who scores goals", he said.
"We've a number of players here who have reasonably good goalscoring records who haven't settled in - [Oumar] Niasse when he came from Russian Federation, but has scored a few this year".
"Niasse, when he came from Russian Federation, but has scored a few this year, and Sandro who hasn't quite settled yet but scored lots of goals at Malaga last year".
The Blues have therefore relied on youngster Dominic Calvert-Lewin to lead the line this season, and despite his impressive work rate, he has only managed to score two Premier League goals this season as Everton have flirted with the relegation zone.
"[Oumar] Niasse has scored a few, Sandro [Ramirez] hasn't quite settled yet, there are people who score goals here but my signings have to be correct and the right ones for Everton and right for my future".
The Toffees have struggled for goals since Romelu Lukaku's departure to Manchester United at the beginning of the campaign, and with Wayne Rooney, Gylfi Sigurdsson and Dominic Calvert-Lewin all inconsistent in front of goal, the club has found itself struggling in the English top flight this season. "You make bad signings, you get the sack".