The 40-year-old, who has also taken charge of Oldham, Barnsley, and Bristol City since entering management nine years ago, is in the running to succeed Shaun Maloney, who was sacked after just 120 days in the role last month, according to The Scotsman.
Johnson spent most of his playing career in England, most notably with Yeovil Town and Bristol City, but he also had stints with Hearts and Kilmarnock in Scotland, winning the League Cup with the latter in 2013.
He took charge of 103 games as Oldham boss and more than 200 as Robins manager, and 78 at the Stadium of Light, with a 51.3 per cent win rate during his time in charge in the northeast. He was relieved of his duties at the end of January following a 6-0 defeat by Bolton Wanderers.
Hibs chiefs made it known that they were prioritising a manager with experience following the failed risk in appointing Maloney, and both Johnson and Appleton certainly fit that profile.
Links with Derek McInnes, Tony Mowbray, and Karl Robinson are wide of the mark however, with Mowbray distancing himself from a return to Scotland and Robinson understood to be committed to Oxford United after leading them to eighth in League One.
Kilmarnock boss McInnes was clear favourite with some bookmakers but there was nothing in those links either.