Posh are looking for a replacement for Jim Gannon, who has decided to quit the Championship's bottom club at the end of the season.
Johnson, 54, left City by mutual consent earlier this month after five years at the helm, during which time he won promotion from League One in 2007 before guiding the Robins to the Championship play-off final the following year.
"I have spoken to Peterborough director of football Barry Fry since leaving Bristol City, but I can't comment any further on the speculation aside to say I'm flattered to be linked with the job," Johnson told BBC Radio Cambridgeshire.
Peterborough chairman Darragh MacAnthony wants to make an announcement regarding the next permanent manager before the end of the campaign.
Posh have had three bosses this season. Mark Cooper replaced Darren Ferguson in November, and was himself replaced by Jim Gannon in February.