McDermott was impressed with Griffin's performances last campaign as well as the help he gave to the club's youngsters and desperately wants him to return to the Madejski for the 2010/11 season.
He told BBC Sport: "We're trying to do something with Stoke and with Andy. He knows my feelings about that.
"We've seen at Reading what a good passer he is and the way he conducts himself with the younger players - they gravitate towards him.
"When we took him there were a few people who weren't sure about him because he hadn't played many games over a period of time. But I remember watching him in two reserve games for Stoke and it shone out to me what a great attitude he had and what a good player he was."