The flamboyant all-rounder wants to spend more time with his ailing father, who is receiving treatment in the United States.
"His brother is in the USA but Afridi wants to spend time with his father and might seek permission from the PCB in next few days," a source said.
Pakistan will be travelling to face Ireland in the two ODIs to be played on May 28 and 30.
Sources also added that Afridi, who left for the USA on May 17, was already depressed due to his shock removal as the captain of Pakistan's ODI team by the PCB.
Afridi was sacked by the chairman of the board, Ijaz Butt last week and replaced by senior batsman, Misbah-ul-Haq for the Ireland series.
Misbah is presently leading the team in the Test series against West Indies.
"Afridi is unhappy with the way he was removed as captain without being given any reason for the decision. He is all the more surprised since he led the team to the World Cup semi final and also to ODI series win over the West Indies," the source said.
Afridi was sacked after he criticised coach Waqar Younis for interference in team selection during the 3-2 one-day series win against the West Indies.
