Chicago, April 25.—A special dispatch to the Times from Cairo on the 25th, saysthat passengers by the Belle of Memphis report that at Savannah they heard heavyfiring in tho direction of Pittsburg. The cannonading was brisk and gradually becoming louder, and was heard lor tniles this side of Savannah.It is the belief that a general engagement is brought on, which is strengthenedby the fact that on Wednesday significant preparations were made by Gen. llalieck for an attack.Our gunboats on the Tennessee riverhad effected a passage over the Muscle Shoals, penetratiug as far as Guntersrille,Ala., where they captured a quantity of rebel commissary stores.