Baggies caretaker boss Darren Moore is also being considered following his remarkable five-game unbeaten run at the helm.
And Lansdown is adamant that Johnson is going nowhere.
"Lee is here for the long term", he told BBC Radio Bristol.
"I know nothing about it, other than what I've read on Twitter or whatever. It's not been mentioned to me.
"I'm not aware that the club has had any sort of approach."