By the RAW, no, but it’s a DM call
There is nothing specific in the rules about readying an action to strike a creature with reach when it comes in to attack with a body part, and the rule is that you can only make melee attacks against creatures that are within your reach. Despite the attacker having a long reach, its body is way over there, so by default, you can’t do this. However, a DM could certainly to decide to allow it based on the situation at hand.
It’s reasonable to say that you can chop at a limb as it comes towards you; but it’s equally reasonable to say that a dragon’s claw is too heavily scaled and moving too fast during an attack to present a target for a melee attack.
Now, if you’re being grappled by an Enormous Tentacle, it’s pretty hard to argue against being able to attack it, since it’s literally wrapped around your body; but again, this is down to the DM and the exact scenario at the table. There’s no official rule that says this is possible, but that’s why we have human DMs at the table.