Knill assumed control of first-team affairs after Mick Harford was sacked last week.
He guided the Millers to a 1-0 win over Bradford, ending a 19-game winless streak.
The Yorkshire side held extended talks with a possible successor for Harford, but talks broke down leaving Knill to remain in charge.
Chairman Peter Ruchniewicz said: "It reached a point where our discussions with one strong candidate in particular reached an advanced stage.
"However, we are no longer proceeding with those talks and it now seems unlikely that an appointment will be made before the New Year.
"We would have preferred to have made an appointment before Christmas but because of circumstances beyond our control it just wasn't possible.
"In the meantime, Alan is doing a good job and has already got one victory under his belt."