dnd 5e – Can you detect telepathic messages in your head, like the Sending spell, via Detect Magic?

Detect Magic (PHB p.231):

For the Duration, you sense the presence of magic within 30 feet of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature (…) in the area that bears magic, and you learn its school of magic, if any. (…)

This questions hinges on the definition of ‘bears’ here, and whether a creature that is being spoken to with sending bears magic:

Bear

  1. (of a person) carry.
  1. support

So is a creature who has had the spell sending cast on them supporting or carrying the spell?

Sending (PHB p.274):

You send a short Message of twenty-five words or less to a creature with you are familiar. The creature hears the Message in its mind, recognizes you as the sender if it knows you, and can answer in a like manner immediately. The spell enables creatures with Intelligence scores of at least 1 to understand the meaning of your Message.

In order for the spell to succeed, the creature targeted must have an intelligence of at least 1, and the creature can respond to the spell immediately. This would imply the creature requires some capacity to support the spell being cast on them, which I believe is enough justification for the creature to ‘bear’ at least part of the weight of the spell, and be detectable by Detect Magic. In order for the Detect Magic caster to determine the source of the magic and spell school, however, they would need to activate the faint aura within the same time frame that the targeted creature is receiving and responding to the spell.