The contract award by client British Land and Oxford Properties is due to be made by the end of the summer and is down to a straight race between O’Rourke and Skanska.
The Enquirer has spoken to leading commercial construction experts who believe O’Rourke is edging ahead in the contest.
One contracting boss said: “It’s a real fight but it seems O’Rourke is determined to win this one and has put in a very competitive bid.
“They have built a lot of concrete cores but this will be the first major office skyscraper for O’Rourke in the City and will be a statement in what is seen as one of the few growing markets at the moment.”
Groundworks have already started on the cleared site and construction work is scheduled to last until late 2014 at least.
Another contracting source said: “The word is that O’Rourke have set their sights on this and when they want something they usually get it.
“They have put a lot of work into the bid and the feeling is they could be more competitive on price than Skanska which should tip the balance.”