Allardyce gave Manchester United defender Jones his debut at Blackburn.
He told the Daily Mail: "It was a huge ask for him to go to Old Trafford and slot in but he has done it. He is incredible. I notice that Alex has him playing at centre half and I think that will prove to be his position over the years.
"We played him in centre midfield at Blackburn for a time as we had Chris Samba and Ryan Nelsen, who were such a reliable central defensive pairing for us.
"I think Alex was on to him from early on. He used to come over to watch Mame Biram Diouf quite a lot. He was on loan to us from United. It was obvious he would notice Phil. When a player is that good, it doesn't take a rocket scientist to notice.
"What his current standing as a United player shows is that he is a very gifted footballer. It also shows what can happen if we allow our young footballers to develop and come through in this country. We don't do that. We don't learn our lesson. Managers feel rushed and buy instead. It's a shame as the talent in our game is there. Phil Jones proves that."