The 21-year-old midfielder will see his current short-term agreement with the Bees expire in January, sending him back to Carrow Road.
The youngster feels it would be of greater benefit to all concerned if he was allowed to stay on at Brentford and take in regular football with a competitive side.
Adeyemi believes Norwich boss Chris Hughton will agree with him, with it also important for him to build up his fitness following a recent spell on the sidelines with a hamstring injury.
"I would love to stay on," said Adeyemi.
"I've really enjoyed my time here. I had a good run of games before my injury - even when I've been on the bench, the manager's looked to get me on.
"But a loan has to be agreed by both parties.
"I spoke to the manager at Norwich and he said he was happy with how things were going. From what he said, it seemed he was happy for me to be here."
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