The 23-year-old American has struggled to force his way into Leeds manager Simon Grayson's plans this season.
Carlisle manager Greg Abbott said: "Mike is a player that we know all about. He's young, full of energy, and he wants to be playing football.
"His opportunities have been limited this season, so he will come here and we think that will give us something a little bit different.
"We can now take a look at him and assess the situation in November."
Grella, who signed for Leeds in January 2009 following a successful trial period, has made just two substitute appearances this season.
Source: PA