A Skanska spokesperson said: "There is an investigation taking place, which we are vigorously carrying out with UCATT as part of our grievance procedures. This will hopefully be resolved quickly."
UCATT South-east organiser Chris Tiff was due to meet Skanska representatives this week to resolve the Carlton Gray case.
Tiff said Gray, who was born in Jamaica, had the union's full support. He said: "We will meet Skanska and may have to consider going to an employment tribunal."
The case comes as an independent report is set to reveal that the number of black and Asian workers in the construction industry has failed to rise in the last three years.
The report, due to be launched at the industry's Respect for People conference on 9 October, shows that black and Asian people are seriously under-represented in the industry. Though they make up 6.7% of the working population as a whole, the proportion in construction is 2%.
The report, by the Royal Holloway, University of London, is a follow-up to a similar report three years ago. The 1999 report found that the proportions were 1.9% and 6.4%.
We are carrying out a vigorous investigation with UCATT
The new report will recommend that construction firms should appoint at least one member of an ethnic minority to recruitment selection panels.
It will also say that more black and Asian university lecturers should be recruited, and that universities should play a greater role in ensuring that black and Asian students have a direct route into the industry after their courses.
Other figures to be released at next month's conference will reveal that ethnic minorities registering for NVQs in construction do so at a later age than white counterparts.