Davis is set to put pen to paper on a four-year contract but Cottagers boss Roy Hodgson will be unhappy with the fee after he told the Glasgow giants to stump up £6million last week.
Davis helped Rangers win two domestic cup competitions last season as Walter Smith came close to guiding the club to a unique quadruple.
He becomes Smith's fourth midfield signing in little over a week following the arrivals of Aaron Niguez Esclapez, Pedro Mendes and Maurice Edu, but too late to keep Rangers in Europe this season.




