The Daily Mail reports that Spurs boss Harry Redknapp has made the bid in order to stop the defender joining Queens Park Rangers.
Redknapp has put a central defender at the top of his January shopping list.
Spurs officials have contacted Rovers regarding a move. Samba is reportedly keen to leave Rovers in the January transfer window.
Queens Park Rangers made a £7million bid for Samba on Tuesday, but they are now set for a fight with their London rivals to land the defender.