They are ready to pounce if Leeds are forced into administration.
According to the Sunday Mirror, Newcastle will offer around £2.5m for a player whose real value must be between £5m and £6m, even in today's market.
The Magpies have already inquired for Barcelona's Patrick Kluivert and Southampton's James Beattie, but any chance of getting Smith in a direct deal with the administrators makes him a better proposition.
"There is no room for sentimentality in football and if an administration order makes Smith available on the cheap Newcastle will go for it," said a source.
"Sir Bobby Robson is a big fan of his and, although leaving Leeds would hurt Smith, a move to Tyneside wouldn't cause too much upheaval. He also knows Jonathan Woodgate and Lee Bowyer and that could be a big factor. Newcastle know Liverpool are interested and Manchester United will probably come in, but Woodgate and Bowyer could sway it their way."