The midfielder has made one appearance in the last three months after suffering a hamstring injury. On his return to action in late November, he picked up a knee injury, though his hamstring problem has been the biggest issue.
“Ben had another injection a couple of weeks ago,” boss Gary McSheffrey said.
“I think it requires a week’s rest, a week of light rehab, then a bit more intense work in the gym and then a week on the grass.
“I think he probably needs three or four weeks from now to even be in contention.”
Close had been on course to return during the festive programme but continued to feel pain on the site of the injury, with the club exercising caution over his return.
Fellow midfielder Ed Williams is currently sidelined with a hip flexor injury.
But McSheffrey hinted the 24-year-old could be set for an exit from the club in the coming weeks.
Williams was welcomed back into the fold when McSheffrey took charge of the side in early December, having previously been exiled by former manager Richie Wellens for three months.
He said: “Ed has got a bit of a hip strain.
“I think he tweaked his oblique playing too much golf. That’s been his number one sport this season.
“He trained with me for a couple of months and he wants to train.
“He might have something in the pipeline in January or February so he needs to make sure he is fit in order to make that happen.”
Though he was named on the bench on three occasions in December, Williams has not made an appearance for Rovers since the Carabao Cup defeat at Stoke City in August.
Ethan Galbraith was forced off injured during Saturday’s defeat at MK Dons but McSheffrey says he is not too concerned about the issue.
“Ethan has had tightness at the back of his knee, the bottom of the hamstring, top of the calf area,” McSheffrey said.
“He had it after the game against Wigan, played through it on Tuesday and it just cramped up on Saturday. Once he went in for something, it just seized up.
“We brought him off as a precaution. We don’t think it’s too bad and we’ll wrap him up this week and get him right.”