TOKYO, Dec 22 (Reuters) - Toyota Motor's small car unit Daihatsu Motor has decided to halt production at all its domestic plants until the end of January, the Nikkei business daily said on Friday, without citing sources.

Following the Nikkei report, a Daihatsu spokesperson said the company was still holding discussions about the matter internally.

The small car specialist said on Wednesday it would halt shipments of all of its vehicles after a safety investigation found issues involving 64 models, including almost two dozen sold under Toyota's brand.

The automaker, which is fully owned by Toyota, has resumed shipments from its subsidiary in Indonesia, PT Astra Daihatsu Motor, the spokesperson said, adding that it was the only unit where the company had done so.

Indonesian conglomerate PT Astra International Tbk and Toyota Tsusho also own a stake in the joint venture. (Reporting by Daniel Leussink and Kiyoshi Takenaka; Editing by Jan Harvey)