Former Sky Blue Greg Abbott who is in charge of the Cumbrians has opted to take the Trinidad & Tobago international until the end of the season.
So far, Birchall has only made one substitute appearance.
"Birchy is not coming back to us," said Chris Coleman to the CT. "He has gone to Carlisle until the end of the season and it is up to them whether they do anything.
"He has got to play so many games for them before a contract kicks in for him there but he is done and dusted at Coventry City."