The motion has been submitted by the opposition bloc and a vote has been scheduled to be held in parliament next Wednesday.
The Daily Post newspaper said the speaker had ruled the motion in order with 31 signatures on it, but it is unclear whose signatures are on it.
However, the government has also spent the day maneuvering, reportedly announcing a series of new appointments in an attempt to shore up its support.
Parliament will sit today at 2pm, local time.
Mr Salwai's government was formed following a snap election in January after half the previous government was jailed for corruption, related to payments offered for support in a previous motion.
Vanuatu politics has been plagued by regular motions since independence, something Mr Salwai's government had hoped to end.