Wakefield-based DLA received detailed planning permission to extend the west stand and south-west corner of the stadium last month and is now consulting with contractors.
However, Leeds Sporting, the club's parent company, this week announced that it is to conduct a feasibility study on the stadium's future with Leeds City Council.
The study will look at whether it would be more cost-effective to develop the existing facility or build another stadium on a new site.
If the club does decide to redevelop Elland Road, it is understood that the west stand project would be the first stage of a three-phase project.
An insider said the west stand extension would cost about £15m and the contractors were keen to forge links with the club so as to be in contention for the second and third phases.
Leeds council confirmed that talks had begun with the club but added that no sites for a new-build stadium had been looked at yet.
The design team for the west stand project includes structural engineer SKM, and quantity surveyor Hall and Partners.