This is one of the fallacies of the fitness world that has plagued the industry for years. Muscle tissue is completely different to fat tissue. A synonymous question would be 'can fat turn into bone?'.
Both tissues have completely different functions. Primarily, muscle generates force whilst fat stores energy within the body. Both tissues can increase or decrease in size. So, you either lose/gain fat mass OR lose/gain muscle mass. The two are completely separate from one another.
This misunderstanding is due to many bodybuilders becoming fatter when they cease their training. Their muscle mass will decrease and no doubt their activity levels will too. As a result, their body will require less calories every day to sustain themselves. But, if they were to maintain a large diet they will acquire body fat - which is often the case. (As a rule of thumb, the heavier you are, the more calories you require on a daily basis and muscle mass requires more energy than fat mass).