Dan McKellar stepped down with a year to run on his three-year deal, citing personal reasons, in a surprise development last month.
Expressions of interest for the vacancy closed last Friday.
It's understood former Waratahs and Wallabies coach Cheika, currently on a one-year deal as an assistant with the NRL's Sydney Roosters, has not yet applied for the role.
The Waratahs' high-performance program is run by Rugby Australia.
Cheika was the first man to win major club titles in the northern (Leinster in 2009) and southern (Waratahs in 2014) hemispheres and won World Rugby's 2015 coach-of-the-year award.
Since his departure from the Waratahs in 2015 they have only played one semi-final, finishing eighth with a 5-9 record this year and struggling to build continuity in their roster.
Waugh refused to say if he had spoken to Cheika about the job, but was open to the prospect of his return to Australian rugby.
Stephen Hoiles, Chris Latham and John Manenti are also reportedly in the mix.
"We want world-class coaches, right across the system," Waugh told AAP.
"That's our focus; there's multiple applicants and we're working through it.
"We want to provide certainty to players and supporters as quickly as we can.
"I don't like to anchor myself to timelines when it comes to coaching announcements, but we're conscious of getting the right person and the importance of a successful Waratahs in a World Cup year."
Waugh added RA would continue to discuss future opportunities with departed coach Joe Schmidt despite the New Zealander lining up work in Ireland as a consultant with Ulster, offering guidance to the province's age-grade coaches.
The role could reportedly see him make multiple visits, while he also committed to be part of the Australia A coaching set-up under Stephen Larkham.
Waugh on Wednesday said Schmidt was "free to do as he pleased" when asked if his return to Ireland had been flagged.
"We've got a very close relationship with Joe and are appreciative of his contribution," Waugh said.
"We'll continue conversations with how he can be involved and have been pretty open about that."
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