The contractor is seeking work independently of the US-controlled reconstruction programme, but it is keeping the British government informed of its movements.
This is the third time that senior managers have visited northern Iraq since the overthrow of Saddam Hussein in May. It is believed, however, that a deal may be some way off as Costain still has concerns about security.
A spokesperson said: "We are looking at the needs [of Iraqis] and how we can be of help. We have certainly made progress with the Kurds. We have people out in Iraq this week."
A source close to Costain said: "The feedback from Costain's international people is that there is tangible progress being made with senior representatives of the Kurdish community but security is paramount if it is going to work there."
Costain has voiced its security concerns in the past. Despite being the first UK contractor to publicly express an interest in pitching for work in Iraq, chief executive Stuart Doughty said in September: "Nobody wants to be in Iraq because of the level of security needed. Until the place is secure, we will not be going there."
Doughty added that he thought the company might start work in Iraq this year.
Fellow UK contractor Amec has already missed out on two major contracts that have gone to US-led consortiums.
Halliburton and Parsons were awarded oilfield contracts worth £1.1bn by the American army last week.
Amec was part of a joint venture with US firm Fluor. The firm said that the failure would not put it off bidding for more contracts in Iraq.
Doughty said the company had completed its recovery process – in the 1990s Costain posted losses of more than £600m.
Doughty said: "The prospects for the group are good and recent contract wins will strengthen future earnings."