The Sky Blues last week revealed that more than 40 candidates had applied to succeed Robins, who left the League One club on February 14 to take over at Championship side Huddersfield.
Coach Lee Carsley has been in temporary control of first-team affairs since Robins' departure.
Development director Steve Waggott said via a statement on Coventry's official website: "There has been a really interesting mix of applications and we have key criteria that we want the next manager to meet.
"We have sifted through applications, spoken to several people for references and are drawing up a shortlist before conducting the final interview process.
"There are several scenarios we are looking at and I am keeping Lee Carsley fully informed on the situation because he is doing an excellent job, along with the other backroom staff who have been ultra professional throughout the last two weeks.
"We have said we will give him everything we can in terms of resources to help us stay in promotion contention, which has included bringing in another defender on loan from Southampton in Aaron Martin and recalling Cody McDonald from his loan spell with Gillingham, while we continue to go through the right and proper process of appointing our next manager."