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Alam claims he has been offered a two-year deal but the Pakistan Cricket Board say the position is on an interim basis while the search for a full-time coach continues.
"Yes (PCB) chairman Ejaz Butt has talked to me and offered a contract for two years... but they will officially announce it next month," the 66-year-old Alam said on Saturday.
Butt, however, countered that other candidates were under consideration for a permanent position.
"Alam will be coach for the Abu Dhabi series but we are considering two or three candidates for a long-term contract," Butt said.
The PCB released former Australian Test paceman Lawson from his contract on Friday with three months' pay as compensation, insisting they were not satisfied with his performance.
Alam, who had been one of Lawson's most vocal critics, said he considered coaching Pakistan as a huge challenge.
The leg spinning all rounder appeared in 47 Tests and coached the Pakistan side that won the 1992 World Cup. His last national coaching assignment was in 2000 when Pakistan lost a home series to Sri Lanka.
He later coached the Indian Punjab team in their domestic Ranji Trophy tournament for two seasons, once taking them to the final.