Experienced midfielder Davis was one of 12 out-of-contract Shrewsbury Town players released at the end of last season.
But the former Birmingham favourite revealed discussions continued with Cotterill and a potential return deal was ‘never off the table’ as the 30-year-old was invited back to pre-season training.
And Davis, who made 21 appearances for Town after checking in on a short-term deal in January, penned a new one-year deal in July.
“I had a chat with the manager at the end of the season. We spoke about various things, and then he spoke to me in the summer about coming to training,” Davis said.
“I hadn’t had anything sorted anyway, so I came in, trained, and there was a deal on the table.
“For me, it was kind of a no-brainer, I enjoyed my time here last year and the gaffer not being here was a big thing. Him being here was a big factor to work with.
“It was great having been settled here and really enjoyed myself.”
Davis is one of just a few natural central midfielders in Cotterill’s ranks and returns to action against Crewe today following a one-game suspension.
The midfielder missed a chunk of football through injury struggles in the back-end of his Birmingham career and was briefly sidelined with a hamstring niggle this term.
He said of returning to training in the summer: “The way I am I always give 100 per cent anyway. It was an opportunity to keep myself ready whether it be here or somewhere else.
“But the opportunity arose and I took it with both hands.
“It was a little bit disappointing (being let go) – but it wasn’t ever off the table, we were chatting and it was never off the table, it was always ‘there could be a chance’.”
The midfielder, who was sent off at the end of an influential display in Town’s sole league win so far this term, said: “I’m raring to go to be honest, I missed three games due to a hamstring niggle which was very frustrating due to how hard we’d worked.
“We suffered quite a few injuries so we haven’t had that rhythm of everyone available. Everyone is chomping at the bit now.