Stoke are prepared to sell the 31-year-old over the summer and Royals assistant manager Nigel Gibbs confirmed Brian McDermott is keen to bring Griffin back to the Madejski Stadium.
"We've always got lists of different players we're interested in," Gibbs told getreading. "But we have thrown our hat into the ring with Andy Griffin and it's no secret how much we want him.
"We will react to the situation regarding him for now rather than being pro-active. Andy was a great signing when we brought him on loan in January. He was one of the most reliable players we had.
"His positional awareness was fantastic and I remember when I went to see him play for Stoke reserves writing exactly that in my notes.
"Brian's knowledge of players from his scouting days is second to none. You're never 100 per cent sure about any signing until they come to the club.
"But we had a lot of good references on Andy from other people. He is a total professional and his experience was vital for the group."