David Norris, Greg Halford, Erik Huseklepp, Liam Lawrence, Dave Kitson, Tal Ben Haim and Kanu remain at the club.
Norris, Huseklepp and Lawrence are close to leaving Fratton Park while Halford is not one of the high earners left on Pompey's books.
However, Ben Haim who is on wages of £36,000 a week, along with Kanu and Kitson are the highest paid players at Fratton Park.
And it is those players who Birch says are crippling the club and damaging the chances of survival.
"Luke Varney has gone and I think there will be two or three more by the end of the week," Birch told BBC Radio Solent.
"So that leaves two or three. But the one or two that are left are likely to be the problem.