Harper was left fuming at the dismissal of Deehan immediately after the Poppies’ extra-time defeat at Leeds in Tuesday’s FA Cup second round replay.
But Harper told BBC Radio Northampton: "I’m more-or-less certain I want to stay at the football club.
"The feedback I’ve had from the fans has just been phenomenal."
He added: "I never wanted to leave. But my assistant was sacked and I felt that was unjust."
Kettering chairman Imraan Ladak admitted he was "amazed" by the fans’ negative reaction to his sacking of Deehan over substitutions made in the latter stages of the cup tie at Elland Road.
But Harper denies there is a problem with Ladak interfering in on-the-field matters.