McGivern joined Hibs last August on loan until January and he has impressed during his stay in Edinburgh.
The left-back has made 15 appearances for Hibs and has quickly established himself as a key member of the side.
Hibs boss Pat Fenlon is keen to keep hold of McGivern and he is in talks with City about extending his loan until the end of the season.
City are happy to let McGivern stay on loan as he is well down the pecking order in Roberto Mancini's plans.
McGivern has enjoyed his stint at Hibs and he is thought to have verbally agreed to stay on loan for the remainder of the season.