Kevan helped the former County boss to steer Stoke to promotion when they worked together at the Potteries club seven years ago.
He admits the prospect of reforming the partnership was appealing but says he could not bring himself to walk out on the Magpies.
Kevan told the club's official website: "After all that Ian McParland and I have been through over the past 18 months, I cannot walk out on him now.
"I must admit the offer from Crewe was very appealing - not least because I live only 20 minutes drive from Gresty Road - and I had to give it proper consideration.
"But deep down I knew I would be staying because our job at Notts County is nowhere near complete."