Woolmer, who took over as Pakistan coach in 2004, died in hospital in Kingston, Jamaica on March 18, one day after his team lost to Ireland and were knocked out of the tournament.
"We are in talks with Whatmore as we are interested in hiring him," Zakir Khan, the Pakistan Cricket Board's Director of Cricket Operations, told Reuters on Thursday.
Australian Whatmore led Sri Lanka to the 1996 World Cup and guided Bangladesh to the Super Eights of the 2007 tournament in which they beat India and South Africa.
Whatmore's contract with Bangladesh ends after the home one-day and Test series against India which started this week.
The PCB last month advertised the position of national coach and set May 15 as the deadline for applications.
Board sources said the 53-year-old Whatmore had not yet formally applied for the post, but Zakir said that would not be a problem if the talks proved successful.
"The thing is we have to see if he is ready to accept any final offer we make to him," Zakir added.
Whatmore, who led Sri Lanka to series wins over Pakistan in 1995 and 2000, has previously said he was keen to work with the Indian team.
Zakir said a number of foreign coaches had sent applications for the Pakistan coaching position but would not reveal their names.
"We have got applications from England, West Indies and Australia," he said.
