New Cappielow chief Shiels was keen to run the rule over ex-Scotland international Riordan as he looks to strengthen his squad before the end of the transfer window next Friday.
But the controversial forward was a no-show at the Ton's Parklea training base this week and has since been linked with a switch to Belgian side Royal Antwerp.
Shiels said: "I don't know where he is. I have not heard from him and he hasn't spoken to me.
"I thought he was coming in this week, but he hasn't appeared. We are now looking at other targets.
"If he is not going to come in then we have to look elsewhere."
Shiels recorded his first win since replacing Allan Moore in the Cappielow hotseat as his side beat Livingston last weekend. And he is keen to build on the momentum of that result.
The Ton host Queen of the South tomorrow afternoon aiming to close the gap on ninth-placed Cowdenbeath in the Championship.
Shiels said: "We did well last weekend and we want to try and gather some momentum now coming off the back of that victory.
"We have to get a result against Queen of the South and not look beyond tomorrow and how other teams are doing.
"The focus has to be on ourselves and what we can control. We need to keep building confidence and we want to add to that all the time."
Meanwhile, Jonathan Page has left the club by mutual consent.