Celts received £9million in compensation from the Foxes and Walker reckons the board should have looked to have brought in the next Rodgers when he exited the club.
Speaking on the Scottish Football Podcast, the pundit said: "I don't think Neil Lennon is going to be there next season.
"It looks as though he will serve out the rest of this season.
"I've been very critical of the Celtic board and their approach - I don't think there's been any succession planning. When you have a manager like Brendan Rodgers, that relationship with the board didn't end well as Rodgers was critical.
"The Celtic board hate criticism and they were delighted when he left to go to Leicester.
"They were delighted to get £9m in compensation. What they should have recognised was that he was a great manager and that he had improved players who were already at the club.
"They should've looked to get the next Brendan Rodgers, the younger version, in much the same way that they scour the rest of Europe for players who don't go straight to the Premier League in England.
"Celtic should be targeting a young coach who has a proven track record of improving players. That is the way a lot of supporters would prefer they went about their business. The sooner they get someone in to do that, the better because there are a lot of changes needed in the Celtic squad."