Stubbs is currently the youth team coach at Everton and was interviewed for the vacancy at Goodison Park last summer before Roberto Martinez took over.
According to Sky sources, the former Celtic defender has been given permission to speak to the Easter Road club about becoming their third manager in less than a year.
Hibs U20 coach James McDonaugh has been put on stand-by to take pre-season training on Monday as the hunt for a new boss, spearheaded by new chief executive Leeann Dempster, continues apace.
Antonio Tapia, a former assistant to Manchester City manager Manuel Pelligrini, is also believed to be on the short list, while Mark Venus, former midfielder Ian Murray and Motherwell manager Stuart McCall have also been linked with the vacancy.
Terry Butcher, who replaced Pat Fenlon in November last year, lost his job in the aftermath of Hib's relegation from the Scottish Premiership at the end of last season.