Carillion has until that day to make another approach to its rival or not be able to make another move for six months under takeover rules.
It is understood that Carillion bosses are mulling an improved offer following a series of rejections by Balfour.
An improved deal could include greater control of the £3bn combined group for Balfour.
The current offer gives Balfour shareholders 56.5% of the merged equity which could be upped to 58.5% under any improved deal.
Carillion issued a fresh statement to the City this morning confirming that its estimate of £175m in annual cost savings has been ratified by independent accountants.
Any merger could see thousands of job cuts as Carillion plans to reduce Balfour’s UK Construction Services division by up to two-thirds.