Shelvey, who is currently on-loan at Championship side Blackpool, has featured for England at youth and Under-21 level.
Adam said: “Jonjo is really interested in playing for us. He wants to represent Scotland – he’s told me he is up for it.
“He told me a while ago he had a Scottish grandad and I said, ‘Why don’t you play for us?’
“We need as many good players as we can if we want to reach the 2014 World Cup in Brazil.
“If Jonjo can improve the squad, why not? It doesn’t matter where he was born. He is eligible and can play.”