Lawson is among three on Pakistan's shortlist for the job, along with compatriots Dav Whatmore and former fast bowler Richard Done, the newspaper report said.
Former New South Wales and New Zealand coach Steve Rixon has told AFP that the Pakistan Cricket Board (PCB) contacted him about the role but he had already made other plans.
Lawson said he also had been contacted, at short notice, about the job and was trying to obtain a visa from the Pakistan High Commission in Canberra. He was hoping to fly out this weekend "once the paper work has been done".
"It's a significant challenge," Lawson told Saturday's The Australian newspaper about coaching Pakistan.
"They're an underachieving team with plenty of talent.
"I'm flattered I've even been invited I suppose. I certainly haven't been chasing it. At short notice they asked me to come to Islamabad for an interview."
Lawson, 49, currently a media commentator, claimed 180 wickets in 46 Tests between 1980 and 1989 before finishing his career as NSW state captain and later becoming their coach.
Done replaced Woolmer as the International Cricket Council's high performance manager two and a half years ago, after the South African took up the Pakistan job.
Done played first-class cricket for NSW before beginning a successful coaching career in Australia.
He worked for nine years as senior coach at the Australian Cricket Academy with Rod Marsh in the development of future international players including Ricky Ponting and Adam Gilchrist.
Done, as the fast bowling coach, was responsible for the early development of the current and former Australia pacemen Glenn McGrath, Brett Lee, Michael Kasprowicz and Jason Gillespie.
Whatmore is aiming to coach a third country after two stints with Sri Lanka and, more recently, four years at the helm of Bangladesh.
Presently in Melbourne with his family, where they are based, Whatmore remains non-committal about his coaching future.
"I've been reading the developments with interest," Whatmore told the newspaper.
Pakistan are searching for a replacement for Woolmer, who died at the World Cup in Jamaica in March prompting a police investigation and controversy.
Police this week announced that he died of natural causes, not murder.
The latest revelations on Pakistan's coaching position come as another Australian, NSW coach and former batsman Trevor Bayliss, was appointed coach of Sri Lanka this week.
Bayliss is the fifth Australian to take charge of Sri Lanka in little more than a decade behind Whatmore, Bruce Yardley, John Dyson and Tom Moody.