The 21-year-old striker did not make it into Sven Goran Eriksson's squad - announced on Saturday - for the friendly against Portugal on Wednesday.
Jermain checked in at the Lane last week and has already netted twice in two games against Portsmouth and Charlton.
Jamie says the capture of the coveted goal-getter is a sign of the direction the club is heading in - and goal will send Jermain heading into the full squad before too long.
"It is a fantastic signing and I'm really pleased," reflected Jamie, who has now featured in two reserve games following his recovery from knee surgery . "I think it shows what way the club is going now and it is great to be part of it.
"The fans have got to be very happy with it. I met Jermain a few times before he joined and he is a great lad who loves playing football.
"He looks like a young Ian Wright to me and he is going to be a great acquisition for us as he is such a good finisher. My Dad managed him at West Ham and he loved him, he said he is absolute dynamite.
"He is different class. If he does well here he will be in the England squad for the summer, no doubt about it. He is a goalscoring machine and there are not many like that."
Club captain Jamie Redknapp predicts new signing Jermain Defoe will eventually break into the full England squad if the goals continue to flow at Spurs.