The 54-year-old told BBC Radio Cambridgeshire: "I have spoken to Peterborough director of football Barry Fry since leaving Bristol City.
"But I cannot comment any further on the speculation aside to say I'm flattered to be linked with the job."
Johnson spent five years at Ashton Gate, winning promotion from League One in 2007 before reaching the Championship play-off final in 2008.
I hope this happens as I'd be very happy with Gary Johnson
CROWE4BARRY
The former Latvia national coach has also managed at Cambridge United, Kettering and Yeovil.
Peterborough United chairman Darragh MacAnthony has told the Peterborough Evening Telegraph that an appointment will be made before the end of the season.
"There is no doubt I will take my time over our next manager. It's probably the single most important recruitment I will make in my time as chairman," he said.
"I would like somebody in place by the end of the season so that the new man can watch our last couple of games closely and gauge an idea of what he will have to work with."
Posh have used three different managers this season. Mark Cooper replaced Darren Ferguson in November, and was himself replaced by Jim Gannon in February.
Source: BBC Sport
Source: BBC Sport