Rodgers has accused Newcastle of taking liberties in their pursuit of Andy Carroll and insisted he would be "a nutcase" to consider a cheap sale.
"Newcastle got £35m for this player last year," said Rodgers. "Even to consider wanting to take him on loan is a liberty. There is nothing more on it for me.
"I need a minimum of three strikers. Once the window shuts, that it is it until January. I have got Luis Suarez, Fabio Borini and Andy. I would need to be a nutcase to even consider at this moment letting Andy Carroll go out, unless there are other solutions for that.
"At the moment there isn't. Andy has been working well. He knows the situation, like the rest of the group do, and we will take it from there. We have a small squad as it is. We have lost a lot of players this summer and I have not replaced them as yet."