Prof Inns also defended the current board and claimed it had the expertise and the experience to oversee the latest rebuild.
The Mackintosh building, in the Garnethill area, was destroyed again after a fire broke out around 23:20 on Friday June 15.
It rapidly spread to nearby buildings, including the Campus nightclub and O2 ABC music venue, which suffered extensive damage.
Prof Inns vowed lessons will be learned from the Scottish Fire and Rescue Service report into the latest fire.
The last restoration project, which cost an estimated £35m, would have taken almost five years with the library reopening in September 2019.
This time round Prof Inns said the project will be helped by a 3D digital model of the original building which was developed after the 2014 fire.
He added: “It could be be that it is somewhere between four years and seven years.
“That’s as much as I can tell you at the moment.”