Allardyce is said to be lining up a £5 million bid for the left-back.
Sam Set For First Signing
The 22-year-old has 11 caps for the England under-21s side, and has his sights on a move to a bigger club.
Baines is said to be gutted that boss Paul Jewell left the JJB Stadium, as he was the man who moulded him into an international player.
Baines is allegedly being watched by Manchester United, Everton, Arsenal and Tottenham, but Allardyce is likely to guarentee him a starting place at St James' Park.