The 31-year-old property developer has revived the Shakers' fortunes off the field since taking over in May by clearing a debt which brought the club to the brink of extinction, compiling a playing squad virtually from scratch and renaming Gigg Lane the JD Stadium in a large commercial deal.
However, that success has not been paralleled on the pitch. Even with victory over AFC Wimbledon on Tuesday night, which was only Bury's second win since August, the Shakers are only three points off the relegation zone.
It remains to be seen whether interim boss Ronnie Jepson, appointed until January, will be handed the reins on a full-time basis but Day believes the calibre of players currently on Bury's books can propel them up the division.
Speaking to the BBC's North West Tonight programme, the Shakers chairman said: "No, I am not worried. We don't talk about relegation here, that's not even in our remit.
"I don't want the players even thinking about that. What we're thinking is that this division is so tight at this moment in time, I think we were only 12 points off the play-offs, maybe 15, 16 points off the top of the division.
"If you put a decent run together you'll be well up there. We've got quality in this side, we need it to gel, we need it to work.
"If you put a run together of three, four games where you win those games, you'll be right up in the top half of the table. That's what we're trying to achieve."
Day, who also revealed there had been over B£1.5million pumped in to ease the financial woes he inherited upon arrival, admits he has learned lessons from the summer's heavy recruitment process.
Bury, then under the guidance of Kevin Blackwell, brought in around 25 new players and Day wants the focus to shift from quantity to quality moving forward.
"We did a recruitment system in the summer where probably we should have done a little bit better," he added.
"That's a learning curve to where we want to be moving forward. We're also looking to recruit all the time, but what we're looking at is bringing in quality players that can actually make a difference to the starting XI."
- Sports & Recreation