Why did Aragorn not tell the Company about Gollum following them ?

[The Mouth of Sauron]

When a few days out from Lorien Frodo finally encounters Gollum at night on the west bank of the Anduin, Aragorn says : "So you know about our little footpad. He padded after us all through Moria and down Nimrodel".

It's surely inconceivable that if Aragorn knew about Gollum following the Company from the West-Gate of Moria onwards, that he didn't at least tell Gandalf. But why weren't ALL the Company alerted from the first moment Aragorn became aware of Gollum ?

[Inziladun]

I don't see that their knowing would have made any difference, save to alarm. They wouldn't have been able to catch him (Aragorn tried), and The Company was keeping a constant watch anyway, so it was unlikely Gollum would have been able to do anything to them.

[alatar]

It's possible that Aragorn thought that telling the Hobbits about Gollum would have been counterproductive. It may have increased their stress, by constantly 'listening' for Gollum the Hobbits may have made it harder for Aragorn to catch him, and as 'the Guide' knew, what's the problem? Gandalf may have even thought it necessary as he might have known that eventually Gollum and Frodo must meet. Letting this information out too soon may have spooked the Hobbits, as later, when Frodo is Guideless, he is more receptive of accepting this new guide, despite all that he knows.