Caretaker boss Russell Milton and assistant Steve Elliott will stay in charge of Cheltenham until May.
The duo took over last Friday following the departure of Paul Buckle, who lasted only three months in the job.
Youth coach Milton and veteran defender Elliott oversaw the Robins' 2-1 defeat against Bury on Saturday, which left them second from bottom in League Two.
The club confirmed a third "experienced figure" would be added to the backroom team next week.
Chairman Paul Baker revealed on Saturday he had been in contact with former Robins bosses John Ward and John Schofield regarding the vacancy, as well as ex-midfielder Grant McCann.
"It's a big step for them and it's important we support them as best we can by bringing in somebody who has a lot of experience under their belt," Baker told BBC Radio Gloucestershire on Monday.
"To bring an experienced head in at this time is the right thing to do. We've shortlisted five or six people and will be speaking to all of them."
Milton has never had a full-time first-team managerial role, but made more than 200 appearances during his playing days at Cheltenham.
Centre-back Elliott has spent the last five years at Whaddon Road but briefly left the club earlier this month after being released by Buckle.
"I think, for various reasons, we've alienated some of the fans in recent months. I want to get everybody back on board now," added Baker.
"Both these two deserve an opportunity now, to see whether they can keep us in the Football League. It's a great opportunity for them to prove themselves in management."