Davies, 36, who was told on Tuesday that his current contract would not be renewed at the end of the season, falls five days short of qualifying for a testimonial match.
The announcement was greeted by uproar from fans in support of a striker who has scored 84 goals in more than 400 appearances for the club.
But Gartside confirmed the player will be given the chance to say a proper farewell to the supporters at the Reebok Stadium.
"If Kevin asks, we'll give him a testimonial. We look after players," he told The Telegraph.
The former England international will be a free agent in the summer, 10 years after joining the club from Southampton back in 2003.