The 51-year old Vasu replaces former India all-rounder Hrishikesh Kanitkar, whose stint as the team coach ended earlier this year after the team bowed out of the Ranji Trophy in the preliminary stage.
It has been learnt that Rathour and Kanitkar are among the four applicants for the NCA coach's job.
Tamil Nadu coach Hrishikesh Kanitkar wants to pick players based on their grit rather than reputation.
Hrishikesh Kanitkar has been named assistant coach of the new Indian Premier League (IPL) franchise - Rising Pune Supergiants.
A left-handed middle-order batsman and a useful off-spinner, Kanitkar represented India in six Tests and 34 One-Day Internationals (ODIs).
"Hrishikesh Kanitkar will be remembered for his contributions for India."
Kanitkar played two Tests and 34 ODIs for India, but was unable to establish himself in the side.
Hrishikesh Kanitkar, who had moved to Rajasthan from Maharashtra, led them to consecutive titles.
India beat arch-rivals Pakistan to create record of highest successful ODI run-chase.
Rajasthan easily took the first innings lead against Tamil Nadu at Chennai.