The bottom line is that you "can't" do that by the rules in 5e - which just means you absolutely can try it, the DM just rules whether and how it works.
Readying an action for something like that would seem pretty extreme, to me - you're giving up your action and anything you could do to prevent an enemy from attacking that ally for it. It also doesn't fit thematically, in combat. Just using a Reaction right at the moment sounds fine to me, the fact you're taking the hit for the ally seem a big enough price to pay.
There's already a way for some characters to give an enemy disadvantage as a reaction. If you wanted to try to save an ally from an attack as a reaction, maybe the DM would let you give the attack disadvantage, at a price - he'd roll 2 dice, if either missed the ally, the ally is missed, but if the other would hit you, you take the hit. Of course, that's assuming you react to the attack before it's rolled. If you react to the hit, you'd presumably have to just take the hit.
One thing about DM-ruling actions like this is that it doesn't make a lot of sense to turn them into some sort of rule. That's a rule-change not a ruling. So it'd be case-by-case, depending on how you describe it and what the DM thinks of it. Some might be a lot harder on you than others.