The PCB has entered into final negotiations with Lawson after deciding to appoint him from a shortlist of three candidates, including fellow Australians Dav Whatmore and Richard Done.
The 49-year-old Lawson, currently working with the New South Wales state team in Australia, played 46 Tests and 79 one-day internationals.
The PCB committee meets on Monday to formally announce the new coach to succeed Bob Woolmer, who died during the World Cup in the West Indies in March from natural causes after earlier fears he was murdered.
The board was initially in favour of Whatmore, who has coached Sri Lankan and Bangladesh, but leaned towards Lawson after getting positive feedback about him from team management and the players, the sources said.
"The board has decided to go along with Lawson as his appointment was backed by the players and also manager Talat Ali in recent meetings with the board Chairman," one source told reporters.
"The players felt that Lawson had a very positive attitude towards the game and was an easy person to get along with."
Pakistan has had eight different coaches since 1996. Former Test captain Javed Miandad has had three stints as coach.
Woolmer, the former England batsman, coached the team from June 2004.