Workers voted to hold one-day strikes on 9 and 16 June after rejecting the original pay offer.
Hanson made a revised offer of a 3.45% pay rise for 2002-3 but this was also rejected.
Bob Blackman, head of construction at the T&G, said the latest offer was the best that could be achieved by negotiations. He said: "I am now recommending that the workers accept the deal but it is up to them to vote to accept it."
The result of the ballot was expected to be announced today.