He told BBC Radio Cambridgeshire: "I thought he might decide to stay, but you never know with Jim what's going through his mind."
"He's done very well and has definitely put himself in the shop window."
Dickinson, who played for Gannon at Stockport as well as Peterborough, admits his own future is also uncertain.
He said: "You've always got to keep your options open as you can never tell what the future holds. I could go back to Brighton and play there, or I could be on the move"
I'll start back again in pre-season and if I'm on the move then I'm on the move
Liam Dickinson
The former Blackpool and Leeds man has scored two goals in six appearances, but his future has been thrown into doubt after Gannon turned down a new long-term contract.
Gannon will leave Posh at the end of the season and Dickinson says he will return to Brighton before deciding on his next move.
"The rest of my season lies at Peterborough and then come the summer I'll be relaxing with my family," he said.
"I'll start back again in pre-season and if I'm on the move then I'm on the move."
Dickinson has not ruled out returning to Posh despite Gannon's imminent departure, but had hoped the 41-year-old Irishman would stay.
He said: "At the end of the day I think everyone's family is the most important thing for them and at this time in his life Jim wants to put them first."
Gannon is aiming to find employment closer to his home in Stockport and Dickinson believes he will not be short of offers.
"A few of the players who had worked with him before thought about putting a cheeky bet on Posh to stay up with Gannon," he said.
Source: BBC Sport
Source: BBC Sport