The former Celtic and Hibernian forward had recently been linked with a move to Royal Antwerp, the Belgian second-tier club, but that did not materialise after their chairman Gunther Hofmans described him as an 'enfant terrible'. The 31-year-old has been without a team since departing Bristol City in December 2012 and had also recently been training with Alloa Athletic.
"We have had [Riordan] in to train; I want to have a look at him," said Carlisle manager Graham Kavanagh. "We are going to have a look at as many as we can, especially those out of contract.
"If we can give someone an opportunity and we feel they are good enough, and are hungry enough to come and improve us, we will definitely take that option up."