The Royals have tried five different players in that position this season, with Icelandic international midfielder Brynjar Gunnarsson currently filling in, despite the fact that he normally plays in midfield.
Reading's caretaker manager Brian McDermott sees the 30-year old Griffin as someone who can bring much-needed experience to his young team.
He is out of favour at Stoke and has only made three appearances for them this season, all in the Carling Cup.
"We need players who know this level," said McDermott. "We hope to progress the Griffin signing soon and I also expect to bring two more loan signings in."