According to Sky Sports, Hibs are within 48 hours of announcing Johnson as their new coach.
Johnson spent six months as a player at Hibs' fierce rivals Hearts back in 2006, but that is not thought to be a factor in the hiring process.
He will take the place of Shaun Maloney, who was fired after only four months in charge.
Hibs endured a poor season last term, failing to reach the top six in the Scottish Premiership and bowing out of the semi-finals of the Scottish Cup.
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