The Reds manager said that the North-East club were taking liberties with the request, adding that he would have to be a "nutcase" to let the England striker go without a replacement in sight.
"There is absolutely no chance [of a loan deal] – and certainly not Newcastle," The Guardian quotes Rodgers as saying.
"Newcastle got £35m for this player last year. To even consider wanting to take him on loan is a liberty really.
"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. That is the reality of where we are."
Liverpool are in Europa League action tomorrow evening against Scottish Premier League side Hearts at Tynecastle.