You can ready the Disengage action but it will almost always be useless
The Ready action states (emphasis mine):
[...] you can take the Ready action on your turn, which lets you act using your reaction before the start of your next turn.
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger [...]
[...] When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
And now let's look at the Disengage action:
If you take the Disengage action, your movement doesn't provoke opportunity attacks for the rest of the turn.
Since the Disengage action is an action, we can Ready it. However, the Disengage action only lasts for the rest of the turn on which you use it. If you use it during your own turn, it only lasts until the end of your turn; if you use it during Bob's turn, it only lasts until the end of Bob's turn. This makes Readying the Disengage action almost always useless, and I'll detail out a bit more why that is:
Say we Ready the Disengage action and use it later in the round on Bob's turn: That means that on the turn we used it (Bob's turn), and only on Bob's turn, we would not provoke opportunity attacks. However, opportunity attacks are only provoked when we move, and it is currently Bob's turn so it is highly unlikely for us to move and benefit from the Disengage action in any way.
The only time Readying the Disengage action has any meaningful effect (besides somehow expending movement on Bob's turn) is if we trigger the Readied action on the same turn we Readied it (our own turn). However, Readying an action and having it occur on our own turn is almost entirely useless since we could have just taken the action itself and we would get to keep our reaction.