Currently assistant manager to Billy Davies at the City Ground, Kelly was a popular striker at Prenton Park during his playing days.
Number two to Davies at both Preston and Derby before taking over at Forest, Kelly is thought to be keen to step up to a top job at some point.
Sunday's newspapers however suggest that Tranmere may shrug off the failure of the Barnes regime and go for another big-name appointment in the shape of Robbie Fowler.