Yes, you can wear contacts instead of the framed glasses in reading. There are two main types of contact lenses designed for presbyopia: varifocal contact lenses and monovision contact lenses.
Varifocal contact lenses might be a good way for you to correct your presbyopia if you have naturally moist eyes. They might also be suitable if you have visual acuity in eyes, are able to focus both eyes simultaneously and no disease in your eyelids.
Monovision is kind of problem using one eye for distance vision and the other eye for near vision. I guess you know what kind of presbyopia you are and find which fits you better. If you don't know it clearly, your doctor will tell you. But if you didn't have prescriptions before, it may difficult for you to adapt to the contacts, so you need learn how to wear them and adapt your eyes to them.
If the above mentioned factors are well, the doctor will check your eyes prescription, including the exact diopter and corneal radius. When you finish all these exams, you can have a fitting except you have the following eye disease: dacryocystitis, serious trachoma, spring catarrh conjunctivitis, keratitis, blepharitis, glaucoma and diabetes mellitus. Hope everything is going to fine!