O'Neill has earned rave reviews for the work he has done and his name is often linked with top jobs that become available.
However, Lerner does not pay any attention to the rumours and is looking forward to working with O'Neill for a long time to come.
"He is in demand, but I expect Martin to be with Villa and I don't see beyond that expectation," the American businessman said in The People.
"I don't think about speculation with other clubs, I think about him with Villa.
"He is an ambitious man, but that's what you want."