The 27-year-old has been a free agent since being released by Hamilton Accies last season and has featured twice for Ton as a trialist.
Moore had been on the lookout for a new goalkeeper after veteran Alan Combe used a clause in his contract to join SPL club Hearts last month.
Hutton's contract initially runs until January and the Ton boss wants his new signing to use that time to earn a longer stay at Cappielow.
Moore told the Tele: "By the time the reserve game comes tomorrow night, David will have signed with us until January.
"That gives us a chance to get a really good look at him and it keeps him on his toes a wee bit. We'll take it to January and see what happens from then on.
"We are obviously a bit short in the goalkeeping department with having just big Derek Gaston in at the moment and this gives Hutton a chance to come in and prove himself. It obviously didn't work out for him at Hamilton, but that sort of thing can happen. We've brought him in to put the pressure on big Derek and push for a place in the first team.
"He's obviously got something to prove and that's what we're looking for - we don't want somebody just to come and sit and be happy to be second choice.
"That's why it is a short-term deal at the moment and we want him to prove himself and then we will see if that can lead on to something longer."
Another player looking to win a deal is former Celtic youngster Liam Gormley, with the striker impressing in a friendly win over Largs Thistle on Sunday.
Gormley will turn out for the Ton reserves tomorrow night with Moore keen to assess his fitness before discussing any permanent move.
Moore said: "He is in training with us so we can have a look at him. He is getting back to playing again and will play again in the reserve game tomorrow. We will take it from there and nothing has been promised. His fitness levels have to come up a wee bit and that's what we are trying to help him with."