The Plymouth player, who had an English mother and a Jamaican father, was called up to the national side in the 1920s but the invitation was subsequently withdrawn.
It would be another 53 years until Viv Anderson became England's first black player.
Former Nottingham Forest and Arsenal defender Anderson admitted he had never heard of Leslie's story until it was brought to his attention in June.
"That's a crying shame because what he achieved and what he did should be paramount in every black person's mind," Anderson told the BBC in July.
There is already a mural to Leslie at Plymouth's Home Park ground and the club named their boardroom after him, but fans wanted to go further.
Having met their original target they want to keep the appeal going.
"Having reached our initial target with such positivity, we are encouraged to go further," said Greg Foxsmith, who is the co-founder of the Jack Leslie Campaign.
"More money enables us to have a bigger, better statue.
"It also allows us to begin work on our aspirations to tell the Jack Leslie story, and use his story to challenge prejudice and discrimination.
"We will continue, at least in the short term, to raise money with our stretch target in place to ensure the best possible memorial to Jack."
Leslie played for Plymouth Argyle from 1921 to 1934, scoring 137 goals in 401 appearances.
He was the only black professional footballer playing in England for much of his career and helped Argyle win a championship and promotion, toured South America and became club captain.
After retiring from playing, Leslie returned to London and resumed his trade as a boilermaker.
He later worked in the bootroom at West Ham United, under future England manager Ron Greenwood.