Rodgers, who replaced Kenny Dalglish as coach in June, was scornful of Newcastle's bid to bring the powerful striker back on loan and said there was no way he would reduce his already limited striking options further with the transfer window starting to close.
"I need a minimum of three strikers. Once the window shuts, that is it until January. I have got [Luis] Suarez, Fabio Borini and Andy Carroll," he told reporters.
"I would need to be a nutcase even to consider at this moment to let Carroll go out, unless there are other solutions for that."
Carroll found some form at the end of last season and forced his way into England's Euro 2012 squad, but he was on the bench for Liverpool's 3-0 opening day defeat to West Bromwich Albion.
West Ham United are also thought to be keen on the 23-year-old but having let forwards Dirk Kuyt and Craig Bellamy leave Liverpool, Rodgers is playing hardball.
"There is absolutely no chance [of a loan deal] - and certainly not Newcastle," the former Swansea City boss said.
"Newcastle got 35 million for this player last year. To even consider wanting to take him on loan is a liberty really."
