The England international is thought to be available if the right offer comes along, but the Reds boss has stated that Carroll will not be going on loan.
The Magpies are thought to have offered around £12 million for the burly hitman, but this has frustrated Rodgers.
“There is no way they will do a number on us,” he told The Telegraph.
“Absolutely no chance – and certainly not Newcastle. Newcastle got £35million for this player last year. To even 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 Carroll. I would need to be a nutcase to even consider at this moment to let 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. It is all speculation. We have got a very small squad as it is. We have lost a lot of players this summer and I have not replaced them, as of yet,” he concluded.
By Gareth McKnight