Documents seen by the Enquirer detail a two year offer of an extra 2.5% from June 2016 and a further 2.75% rise from June 2017.
The offer covers more than 500,00 workers under the Construction Industry Joint Council Working Rule Agreement.
The employers have given union leaders until May 27 to agree a deal.
The unions have already dismissed an earlier offer of 3.5% over two years as “insulting”.
An employer source said: “This is an above inflation pay offer and higher than other industry agreements in terms of the percentage rise.”