On your CV? Completely. (Though there are ways of telling the truth that are better than others)
But when you’re dealing with third parties, especially agencies, then you do not need to share everything. Having operated in recruitment ourselves for many years, let me tell you a typical scenario that can really harm your chances of getting your ideal job.
The typical scenario goes something like: you are a very capable candidate who has two or three opportunities on the go. You have been offered a job, or are strongly in the running for one, through an agency who has introduced you.
You mentioned casually that you are also in the running for a job with XYZ Ltd. Perhaps you have been introduced to them by somebody else or even a friend.
Here is the agency’s dilemma. They know you are a strong candidate for one of their clients, but also for someone who they are not dealing with. Agencies range from the very ethical, that is like how we always wanted to behave, to the very “sharp”.
A sharp operator will not be able to let this go. As soon as they have put down the phone they will make the following judgement, you are 50-50 between their client and XYZ Ltd. If they can get one of their candidates into XYZ Ltd, they have the potential to make two placements. Clearly it will halve your chances of getting your next role, but for the sharp operator that is not their concern.
It happens a lot more than you would believe. And especially in the current climate, where new roles are difficult to come by. If they can get a lead on someone who is definitely recruiting, many will follow it up.
So my advice to you is simple, if you want to be open and upfront with an agency you trust by all means tell them you have a couple of opportunities in the pipeline. But never reveal the identity.
The harder they push you, the more you know they want to contact the client themselves. You are under no obligation to tell them, and if I were you I would insist that the role is extremely confidential and it would be a breach of trust to reveal the identity. End of conversation.
In the meantime good luck, I’m delighted you have two job opportunities.