The 26-year-old spent four years at the Dumfries club before leaving this summer after failing to prevent his side from suffering relegation.
A former Celtic youth player, Reid also spent a short spell playing under Moore while on loan at Stirling Albion in 2007/08.
The Ton boss is eager to add to his defensive options and believes Reid - who can operate as both a centre-half or right-back - fits the bill.
Moore told the Tele: "We are looking into that one just now. At this moment in time he has come in to have a look at the set up and we are having a look at him.
"We are still in the process of trying to get something done there - I obviously know him from when I took him to Stirling on loan a few years ago.
"We want to try and add to our defence and we need a centre-half and a right-back to come in to add to big Mark McLaughlin and Willie Dyer."
However, the Ton boss concedes any hope the Cappielow club might have had of luring Simon Mensing to the club have ended.
The former Hamilton midfielder has served as a trialist at the club but seems intent on pursuing a move to England.
He said: "We've also got another few boys in to have a look at and one of those has been Simon Mensing.
"We've been impressed with him but that might not happen now as he has wants to go to England to play his football.
"We've had Martin Hardie in as well. So we've got quite a few but we are still in the process of picking the right ones.
"We have a little bit of youth in the squad and we also wanted to get some experience to go along with that. We will try to get a good mixture."