Jepson stepped into the breach when the Shakers dispensed with Kevin Blackwell earlier this month and although the team failed to score in his first two games in charge, he has been given until January to prove his worth.
After a summer in which over 25 new players were brought in at Gigg Lane, Day is determined to bring some stability to proceedings and pointed to Jepson's popularity in the dressing room as one of the key reasons behind his extended stay.
"Kevin, as you know, brought players into the club and we recruited quite heavily in the summer," he told talkSPORT.
"What we thought we needed at this moment in time was stability within the club.
"Ronnie had got a lot of the senior players on his side and we wanted to keep that stability.
"We've tried to change one or two things around, create that stability and hopefully kick on to have a successful season."
Jepson has suggested he would like to be considered for the vacancy on a long-term basis and staked his claim with Bury's 2-1 win over Wycombe last time out.
Asked if Jepson could earn the position past the new year, Day added: "If he wins four on the bounce and we end up getting into the top three then certainly."
For the meantime, though, the Shakers chairman is focused on bringing order to a club which he saved from the brink of extinction earlier this year.
He said: "We took over the club at the end of May, paid all the debts off and tried to get the club on a financial footing where it has this stability and it doesn't go up and down in a yo-yo situation owing debts out to other people.
"We're trying to run this a bit more like a business, off the pitch."