The Yorkshireman has been offered a deal by League One outfit MK Dons, but Newcastle will continue to pay the bulk of his £60,000 per week wages.
Smith has played just six minutes of action this season for the Magpies and tumbling down the pecking order in the last two seasons.
Smith joined the club for £7million from Manchester United in 2007 and was one of Mike Ashley's first cash buys.
He has been offered many chances of a move away from St James' Park but he refused because he would not take a wage cut.
Newcastle's odds for the FA Cup prior to game with Brighton:
7/1 Man Utd