Frecklington, 24, told BBC Radio Cambridgeshire: "I think his record since he has been here has proved how much the lads want him to stay here.
"If he does stay it can only be beneficial for all the players and the club in general."
Gannon is only on a deal until the summer and spent Monday in talks with Posh owner Darragh MacAnthony.
I really hope he signs, he could be the best thing to happen at Posh for a very, very long time
PoshFella
The former Stockport man says he is happy with the terms he has been offered, but is unsure about relocating his family. Peterborough chairman Darragh MacAnthony insists Gannon has as much time as he needs to decide his future
Frecklington has become a important player under Gannon, starting six of the last nine matches.
"People can see from our recent performances that our pride has been restored and hopefully we can continue that with Jim for the long term," he said.
Gannon has already overseen four wins as Posh boss, despite losing a number of players to injury and seeing captain George Boyd loaned to Nottingham Forest.
Frecklington says organisation has been key to their recent success, with Gannon ensuring flexibility and versatility throughout the squad.
"Everybody now knows what they're doing and when they are asked to do a different role everyone understands everyone else's position," he said.
"We have been unfortunate with injuries and I think it's important we can cope, and over the past few performances that has been the case."
Posh travel to Forest on Saturday with Frecklington still struggling with a calf problem he picked up against Sheffield United.
"It's touch and go at the moment and it's frustrating as I was having a good run in the side, but you can't do anything about it," he said.
Liam Dickinson (hamstring) and Aaron Mclean (knee) are also likely to be ruled out, while Chris Whelpdale continues to battle with a groin injury.
Boyd cannot play against Posh owing to the terms of his loan agreement, which Frecklington admits is a relief.
"It's good news for us as from what I've heard he's been thoroughly enjoying his time there. It's certainly a great opportunity for him," he said.
Source: BBC Sport
Source: BBC Sport