The Turnbull government's plan to scrap the 457 skilled migration visa faces new hurdles in the Senate with the Greens set to refer it to a committee to examine if it could harm the economy, hobble individual businesses or put at risk Australia's multicultural fabric.

Trade spokeswoman Sarah Hanson-Young will move on Monday to secure crossbench and opposition support for an inquiry into the replacement of the 457 class with a pared down system with fewer eligible occupations and shorter visa periods, and which is separated from subsequent citizenship eligibility.

Greens Senator Sarah Hanson-Young will seek support for an inquiry into 457 visa changes. Credit:Alex Ellinghausen

She is confident of obtaining a majority in the Senate to establish the inquiry on the first day of the Budget session because Labor has argued the government's approach is not properly thought through.

However, a successful referral to the Senate Standing Committee on Education and Employment would need the support of four more crossbench senators.