In Book 16 of The Odyssey, Odysseus and his son Telemachus plot how they will subdue the many suitors who have taken up residence in his home, waiting for Penelope to accept that Odysseus is dead and choose one of them. Meanwhile, the suitors are consuming all of his food and wine (and being rude to strangers and beggars, as Odysseus has already visited his home and was insulted and attacked).
After Odysseus and Telemachus have laid out the plot to quietly remove most of the weapons from the great hall in preparation for their surprise attack on the suitors, Odysseus adds this:
There is also another matter; if you are indeed my son and my blood runs in your veins, let no one know that Odysseus is within the house—neither Laertes, nor yet the swineherd, nor any of the servants, nor even Penelope herself. Let you and me exploit the women alone, and let us also make trial of some other of the men servants, to see who is on our side and whose hand is against us.
He suggests that he isn't sure who is to be trusted, including Penelope herself. She has admitted to him that she still waits for Odysseus to return and expects him imminently, but he seems, at the very least, to fear that she might accidentally betray his identity to the suitors before the plan is complete. He doesn't mention it here, but there's also the possibility that she would try to help him (and his small group) in his vengeance, thus endangering herself.
Athena is also in on his plan and clearly approves of it, because further in Book XVI, we learn that:
Athena therefore came up to Odysseus, turned him into an old man with a stroke of her wand, and clad him in his old clothes again, for fear that the swineherd might recognize him and not keep the secret, but go and tell Penelope.
Keep in mind that Odysseus is the "new" Greek hero, not renowned for his strength and speed and bravery in battle (like Achilles or Ajax) as much as for his shrewdness and cleverness. He wants to make sure nothing goes wrong in his plan, and Penelope is a possible weak link in the plan, should the intelligence of who he is leak out.
In Book IXX, the nurse accidentally discovers Odysseus' identity and turns to tell Penelope who he is, but is unsuccessful "because Athena had bemused the queen, so that she took no notice, paid no heed." Athena thus agrees with Odysseus' plan.