Dugarry becomes a free agent in the summer and after some superb performances while on loan at Blues from Bordeaux other clubs are believed to be interested in signing the French striker if he decides not to stay at St. Andrews.
However, Savage has revealed that Dugarry has given him his word that he will sign for Blues on a permanent deal.
"Christophe has promised me he will stay at Birmingham - and I think he will. He is a man of his word and I believe him," Savage told the BBC.
"He has been awesome for us. People were criticising his goal-scoring record and now he has got four goals in three games. His performance against Southampton was unbelievable.
"But he is also a very nice man as well as being a brilliant footballer and he has fitted in here brilliantly.
"His ability and talent can't be questioned - but I think he has also proved that he is suited to the Premier League.
"Different players are suited to different leagues but Dugarry could play anywhere. He has the skill and technique but also the determination and attitude to work hard.
"He has certainly lifted me and a few of the other lads feel the same way. When you look at the team-sheet and see Dugarry lining up alongside you, it gives you a boost."
