The 35,000 sq ft speculative office, Kings Point, in Oldham town centre is now expected to be complete by the end of the month or early February, according to a director at GVA Grimley.
The five-storey office building was partly funded by the European Regional Development Fund and has attracted some "indigenous demand."
Christopher Cheap, director at GVA Grimley, said: "We're talking to a number of names showing interest. The offices have raised the bar because there has been a lot of indigenous demand as it offers possibly the best Grade A office space ever to be built in Oldham.
"It's anticipated Kings Point will not be completed until the end of the month, possibly even February now."
GMPVF, which started work on the £5m site in May last year, is administered by Tameside council on behalf of the pension fund of the ten Greater Manchester authorities.
GVA Grimley is sole letting agent for the Kings Point.