The 25-year-old joined the League One club in January after struggling for opportunities at the Walkers Stadium.
He has been a virtual ever-present under Posh boss Darren Ferguson, though, making 14 starts since his arrival.
"I'd definitely like to stay beyond the end of the season," Kennedy told BBC Radio Cambridgeshire. "It's been a topsy-turvy season and I'm starting to find my feet here."
Kennedy made the move from Rochdale to Leicester over the summer, but managed just four appearances for the Foxes before rejoining Dale on loan.
He added: "I went to Leicester but it didn't work out and it wasn't very enjoyable. But Darren (Ferguson) has a lot of faith in his players and even if you have a bad game he gives you plenty of confidence."
Source: PA
Source: PA