TikTok shut down operations in the U.S. on Sunday.
On Friday, the U.S. Supreme Court dismissed an appeal against the law banning TikTok.
The Supreme Court verdict dismissed opinions that the law banning TikTok violates freedom of speech.
Justices of the top court had agreed to meet on January 10 to discuss the case, but Zhongshan’s request for additional time, if granted, would delay their ruling.
Mr Trump will assume power as U.S. president on January 20 as a convicted felon.
Mr Alito, a conservative, said the call was about William Levi “regarding his qualifications to serve in a government position.”
The Supreme Court has directed prosecutors to respond to Mr Trump’s application by Thursday morning.
TikTok is already banned in India, Iran, Nepal, Afghanistan and Somalia, with the U.S. moving to join the list after Congress passed a bill to ban the app.
The move highlights the case’s importance, as it involves balancing free speech rights with national security concerns.
It is up to the Supreme Court to grant or deny the writ, but senior judges will look into the judgment if it is okayed.
