The fate of the planned merger between Sony Group Corp.’s India unit and Zee Entertainment Enterprises Ltd. may be known as early as next week, according to people familiar with the matter, as the companies face a looming deadline to resolve their standoff or scuttle a long-awaited deal to create a $10 billion media giant.

Unless the two sides can agree on who’ll lead the merged entity and give the final touches to the merger, Sony is likely to send a letter next week to Zee saying the stipulated demands for the merger couldn’t be met, said the people, who asked not to be named as the information isn’t public. That could be the death knell for the deal since there won’t be enough time to tie all the loose ends by the formal Dec. 21 deadline, the people said.