The Royals face Manchester United at Old Trafford on Monday in their fifth round FA Cup tie and McDermott thinks Giggs has what it takes to follow in the footsteps of Sir Alex Ferguson.
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"I met him at Burton," McDermott told the Daily Mirror. "He was doing his pro-licence and he has all the ingredients to be a top manager.
"I was really impressed, he came up to me and shook my hand. He is humble and quiet.
"I asked him how many medals he had won. He was very blase and just said 12. I asked what he did with them all and he said they were in museums. He was a polite man.
"I’ve read a lot on Bill Shankly and what he did - Jock Stein, too. Sir Alex Ferguson also has to be right up there.
"From when he took over to where they are now is incredible. I have a lot of time for him."