Riordan, who is a free agent, is currently training with the League One outfit as he looks to find himself a new club.
The Scotland international has been without a club since leaving Bristol City in December 2012 and Carlisle boss Graham Kavanagh is ready to offer him the chance to win a deal at Brunton Park.
"We have had (Riordan) in to train - I want to have a look at him," said Kavanagh.
"We are going to have a look at as many as we can, especially those out of contract.
"We would be foolish not to, with the market we are in - we are never ahead of the game in terms of being able to pay the biggest wages.
"If we can give someone an opportunity and we feel they are good enough, are hungry enough to come and improve us, we will definitely take that option up.
"There is nothing to divulge at the moment, he is just training."