The veteran player joined Morton on a short-term deal in October and has made seven appearances - captaining the side in a win away to Ayr United on his debut.
But Kevin McCann has not been offered fresh terms and joins loan goalkeeper Dominic Cervi on heading through the exit door.
Former Hibernian full-back McCann joined Ton in August following a successful trial, turning out for the Cappielow club on 13 occasions.
However, the 24-year-old was left out of the match day squad to face Ayr on Monday and the Ton boss admits he already had ample cover in his position.
Moore told the Tele: "We've let Kevin go as we've got cover in that area of the pitch and if we were to bring somebody else in then we have cover at right-back.
"Grant Evans can play there and big Andy Graham can play there - we just didn't see it as being possible to keep Kevin.
"We've spoken to Derek about a new deal but he couldn't get through [yesterday] because of the weather conditions so we will see how he feels.
"We're hoping that he'll stay - it looks as though it is going to be pretty positive, he just couldn't get down because of the weather.
"It is not signed and sealed, of course, so I will probably know a bit more about that [today].
"Big Dom has obviously gone back to Celtic as well and Colin will now come back between the sticks and he and Matty [McGinley] will fight it out for the first-team jersey."
McGinley has been out of action since November after breaking his hand following a freak training ground accident.
However, the 22-year-old has now recovered and Moore is pleased to maintain the competition for the Ton goalkeeping position following the departure of Cervi.
He added: "Matty's hand is fine, it's cleared up and he is now back in full training so he will compete with Colin for a place in the team."