Johnson has been out of work since he was sacked by the Black Cats at the end of January, following a 6-0 defeat at Bolton.
According to the Daily Record, Johnson, who has also managed Oldham, Barnsley and Bristol City, has been identified as the top target at Easter Road.
Hibs sacked Shaun Maloney, who replaced former Sunderland boss Jack Ross last year, in April after just four months in charge.
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It’s now being claimed that Johnson is close to being appointed, though, and will be assisted by long-term No 2 Jamie McAllister.
Johnson was recently asked about his time at Sunderland, which lasted just over a year and saw the Black Cats win the Papa John’s Trophy at Wembley.
“I loved it,” he told Sky Sports.
“I feel very privileged to have had the honour of coaching what I see as an iconic club in the country, an absolutely fantastic football club with great people, a fan base which is phenomenal. They are churning out 34,000 in League One on a regular basis.
“I think in general terms we did an excellent job, there were a lot of successes in that period and I wish them all the best and am rooting for them to get promotion this year.”