It had been suggested that Gannon would play an important part in appointing his successor.
But he told BBC Radio Cambridgeshire: "Barry Fry and the chairman keep me informed, but I won't have a massive role in the recruitment process."
Posh owner Darragh MacAnthony has stated he wants to have a new manager in place before the end of the season.
League One is our level and as long as there is some pretty football and a few wins thrown in I'll be more than happy
RoweRoweRoweYourBoat
The club started the season with Darren Ferguson at the helm, but he was replaced by Mark Cooper in November, with Gannon taking the helm in February.
"Despite the 60 odd applicants that's been touted about, I'm sure the club will have narrowed that down," Gannon added.
"The chairman and Barry [director of football] need to make a really well informed decision and make sure they get the right manager to bring this club forward."
Former Bristol City boss Gary Johnson has confirmed he has spoken to Fry since leaving Ashton Gate.
Gannon says he would be an ideal candidate given his track record at City and Yeovil Town.
"Gary is a good manager with a good record in League One and the Championship and a good record in promoting young players," he said.
Posh could be relegated on Saturday if they lose to Newcastle and both Watford and Sheffield Wednesday win.
Liam Dickinson (hamstring) is set to return to the squad, but Ryan Bennett (ankle) has suffered an a set-back in training.
Kerrea Gilbert and Gabby Zakuani have been struggling with illness, while Chris Whelpdale and Craig Morgan are definitely out.
"We haven't talked about relegation this weekend, but I'm sure the players will have looked at the league table and considered it," Gannon said.
Source: BBC Sport
Source: BBC Sport