There were claims Malacia was left unhappy being blocked from leaving United in January.
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The Holland fullback has been in the matchday squads of all three of Carrick's games in charge so far and the manager told MUTV: "Of course, all the boys have been, honestly, fantastic.
"They are all desperate to play.
"For Ty to be back, he’s obviously missed a lot of football over recent years, so to be back around the group, he’s chomping at the bit to play.
"It’s really important we’ve got a strong group, as strong as we can, to take us through to the end of the season. So everyone is going to be important in different ways.
"The squad is settled now. We know what we’ve got, which is great. Stability is important for us and we’ll keep moving forward.”