It is understood the project is being delayed due to the fit-out of the upper level of the arena, although the two-time Stirling Prize-winning practice is not involved with this part of the scheme.
However, a spokesman for the arena said the setbacks would not delay the building's opening.
The convention centre is supposed to open at the same time as the city's 2008 Capital of Culture celebrations kick off next January, and it is thought the problems will not affect this.
The spokesman said: 'The situation is that one of the levels in the convention centre side of the arena is running six weeks behind schedule.
'The problem is down to one section of the upper level, and I would say it is less than one-eighth of the whole project. The arena will still open on January 12 when the celebrations begin, and the first convention is still booked and ready to go in February.'