Defoe is frustrated at a lack of playing time at Tottenham and is ready to leave the club in January.
When asked about a move for Defoe, Allardyce said: "I can't really comment on that because don't forget if I comment on having an interest in a player that can be deemed as an approach and they could bring me up on an FA charge.
"Many a manager has been brought up on that over the years. I was flabbergasted when that first charge was made, against David O'Leary, if I remember rightly, saying 'if that player's available I would like to sign him'.
"I don't want an FA charge. They have already had some of my money which they shouldn't have had - they are not having any more."