The announcement comes the day after former Pakistan Cricket Board (PCB) chairman Najam Sethi withdrew his candidacy in response to the ICC's decision the post would only be open to leading former players from July 2016.
Abbas, who was principal advisor to Sethi at the PCB, played 78 Tests and 62 one-day internationals for Pakistan in a distinguished career.
The 67-year-old was the only batsman from the sub-continent to score 100 first class centuries in first-class cricket.
"PCB chairman Shaharyar Khan and board of governors have approved the nomination of Abbas as ICC president for 2015-16," the body said in a statement.
Abbas's nomination will be considered in an ICC board meeting to be held in Barbados from June 22-26. If approved, he will take over on July 1 for one year.
The post of ICC president has become largely ceremonial after the body passed reforms last year which made the chairman the head of the organisation.
The reforms gave India, Australia and England major power and revenues as the "big three of the game".
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