No, at the time counterspell is cast, there is no ready action to trigger.
This answer assumes that the enemy can see you, that you are not under full cover, and that the enemy can tell you are casting a spell.
You attempt to interrupt a creature in the process of casting a spell.
You must completely and successfully cast a spell before it can be considered prepared. However, this is an issue because counterspell actually interrupts the casting of the spell. And because it interrupts the casting of the spell it also interrupts the readying action itself. So, counterspell is actually cast before there is any readied action completed. Without any readied actions complete, there is nothing for counterspell to trigger.
I'll break down the progression for the case in which counterspell fails and the one where it succeeds.
Counterspell succeeds
If the counterspell succeeds, you have lost the spell and the potential readied action like one would expect.
- Wizard A begins to ready action by beginning to cast a spell.
- Wizard B sees the spell starting to be cast and casts counterspell in response.
- Counterspell succeeds and the Wizard A's spell is lost. The action used to try to ready the spell is also lost.
Counterspell fails
If counterspell fails to interrupt your spell, your readied action would then become complete, because the casting of the spell was completed.
However, because the counterspell was cast before the readied action was complete, it would not trigger in response to the counterspell.
- Wizard A begins to ready action by beginning to cast a spell.
- Wizard B sees the spell starting to be cast and casts counterspell in response.
- Counterspell fails so the spell completes.
- The spell is now readied, but nothing happens because counterspell was cast before the readied action was complete.
- If Wizard B casts another spell before the start of your next turn, you may use your readied action against that in accordance to how you set the trigger.