The Terriers sacked Simon Grayson just over a week ago and placed academy manager Lillis and professional development coach Steve Eyre in temporary charge.
Lillis and Eyre's first game ended in a 1-1 draw with Leicester in the fourth round of the FA Cup and they steered Huddersfield to their first success in 13 league games in last week's 1-0 home win over Crystal Palace before their third game at the helm ended in Saturday's 3-0 defeat at one of Lillis' former clubs, Derby.
Lillis confirmed he would be speaking with Huddersfield chairman Dean Hoyle early this week.
"We will come back in on Monday and get back to work in preparation for Cardiff next Saturday," he said after the match.
"I will speak with Dean and the board on Monday and if they give me the green light then we will look at the squad and select a team that we believe can beat Cardiff."
Former Southampton manager Nigel Adkins was installed as favourite to become the club's fifth permanent manager in as many years, while Owen Coyle, Mark Robins and Karl Robinson have all been linked with the job.