Not from that sound alone. A dog may be excited, looking for a place to put a valued toy or showing discomfort. There is no single meaning for a whine. Watch the whole dog. Are they relaxed and able to put it down, or pacing, guarding, panting and unable to settle? Avoid reaching into their mouth or chasing them to test whether they will share.
Give them access to a quiet place where they can choose to rest with the toy. If another dog approaches and they stiffen, separate the dogs and their valued items. The article on a dog's quiet space helps set up a retreat, not diagnose why this particular toy matters. If they growl when approached, use barriers and ask a qualified reward-based behavior professional for a safety plan.
A sudden new whine, reluctance to eat, pain, or frantic behavior warrants a vet check. If the toy is broken, has a loose squeaker or could be swallowed, prevent access safely. If the dog is guarding it, ask a qualified professional for an individual way to remove the hazard rather than reaching in. Do not force a trade at close range when they are guarding.
Today, observe whether the dog can settle and whether the toy is intact. Offer space first. The answer may be as simple as leaving a comfortable resting place, but their body language decides the next step.
Sources: Dogs Trust on stress and frustration signs, Dogs Trust on safe management of valued items, VCA on pain-related behavior changes.