The paper says Shearer has had tests to examine how heading the ball has affected his brain.
"They were pretty nerve-wracking. I have got a terrible memory. I don't know if that is because I don't listen but I have got a poor memory.
"When you play football as a professional you expect in later life you are going to have problems with your knees, your ankles or your back like I have.
"But never did I think playing football could be linked to having a brain disease. That is why the research has to be done."
Shearer believes more research needs to be carried out and greater support for ex-players with dementia should be on offer.
"The authorities have been very reluctant to find out any answers," he said.
"They have swept it under the carpet, which is not good enough.
"Football must look after old players with dementia and put an end to this sense that once you are done playing, you can be put on the scrap heap.
"It's a tough game, it's a brilliant game but we have to make sure it's not a killer game."
