The ex-England boss wanted to bring the Gabon international to England in January last year and was encouraged by his desire to move to the Premier League.
However, a deal proved to be too costly for the Goodison Park outfit and Aubameyang eventually clinched a club record £56 million move to the Gunners.
“Aubameyang was desperate to come to the Premier League and we didn’t really know if it was definitely a yes [to Everton] or not – but it was probably not,” Allardyce told talkSPORT.
“The rumours were that he really wanted to come to the Premier League and he was desperate to come. Whether that could have happened or not, we never got that far.
“It was always going to be too much money for January, because of what the club spent previous to me arriving.”
The 29-year-old has proved to be a big success in English football, scoring 26 goals in 42 appearances for Arsenal in less than a year.