Hart currently has out-of-favour Davy Oyen, inexperienced Gregor Robertson and right-footed Wes Morgan to choose from with the latter currently holding down the first-team place.
It was thought Newcastle's Robbie Elliott was most likely to move to The City Ground on a loan deal but he decided otherwise and it now leaves Forest with an unwanted headache.
Ian Harte was dropped by Leeds manager Peter Reid prior to the 4-0 defeat at Leicester and was sent off for Leeds reserves the following night against Liverpool.