No, there is no single book - or even a collection of them that contains ALL possible chemical reactions. Even within chemistry subdivisions (Inorganic, Organic, Biochemistry) it may not be possible to find a single collection of all possible reactions. In fact, continuing research is finding NEW reactions to this day!
We DO know quite a bit about chemical reactions, so if there is a specific compound, element, or group of compounds whose possible interactions you are interested in, you might find more helpful information by looking at possible reactions of just those compounds.
Bathalang, it's very true that we keep finding new reactions every day. But if you are thinking "Dang, why don't chemists write this stuff down in one place?"-- well, we do, as fast as we can add volumes to Beilstein's "Handbook of Organic Chemistry" and Gmelin's "Handbook of Inorganic Chemistry". These are multi-volume encyclopedias that try to capture every reaction that has ever been written in a textbook or in a scientific article. Every year or so a new volume comes out. To look for the reaction you are interested in, Gmelin is organized by element and Beilstein is organized by the kind of organic compounds that are reacting (you just call them by the original editor's name, each encyclopedia has been going for more than 100 years). Each volume of new reactions is organized the same way, so you can go back to the previous volumes.
You would find collections like Beilstein and Gmelin in big downtown public libraries and university libraries. You can get them on line but there's a subscription fee; go to a big library that subscribes. There are also collections for all the crystal structures ever found (one collection is called "Pearson"), the heat of any reaction you want to write down, the rates of any reaction as long as it has only two reactants and they are both gases, etc. Make friends with a reference librarian.
If that's more than you want to read (but I'll bet you are glad it really is written down!), you might want a one-volume "advanced, descriptive" textbook for graduate students, as opposed to an introductory text for college freshmen. F.A. Cotton and G. Wilkinson wrote "Advanced Inorganic Chemistry". New editions of "Cotton and Wilkinson" keep coming out as more reactions are found. And an old favorite is "Advanced Organic Chemistry" by Louis and Mary Fieser. Louis and Mary are no longer with us and we know-- literally-- a million more reactions now, but if you run across "Fieser and Fieser" in a bookstore, take that puppy home!
An interesting question to which several people have contributed responses., But here is what is known as a back-of-the envelope calculation you might enjoy working on. Chemical Abstracts Service (CAS) creates a unique number for each chemical compound. Several years ago, they reached the point where there were 100 million unique substances. Assume that you take them, two at a time, and try to compile the "book" of all possible reactions. It would have 100,000,000 times 100,000,000 entries. Or 1 followed by 16 zeros: 10,000,000,000,000,000 entries. Assume that each page of your book is 8.5 x 11" and that each of the 10E15 entries is two inches tall. How many pages would this take? Calculations such as these are known as "Fermi calculations."