PCB Executive Committee Chairman Najam Sethi said on Monday he had been in touch with the West Indies Cricket Board (WICB) on the matter, and the Caribbean cricket governing body were keen on the move, reports CMC.
"West Indies have asked to make satisfactory security for the team," he said.
He added: "We gave a proposal to WICB that after West Indies' tour (against) England on March 9, they can visit Pakistan between March 11 to 15."
In return, Sethi said the PCB would give the green light to a request from the WICB to play two T20 Internationals in Florida at the end of March.
The West Indies recently played a full series of three Twenty20 Internationals, three One-Day Internationals and three Tests against Pakistan, but all games were scheduled in the United Arab Emirates (UAE).
The PCB had requested the limited overs games be played in Pakistan but the move was turned down by the WICB.
No major Test-playing nation has toured Pakistan since 2009 when a bus carrying the Sri Lankan Test side was attacked by militants. Several players were injured and policemen killed in the terrorists' gunfire and attack.
The security situation has remained volatile, however. Last March, a suicide blast killed 69 people and injured over 300 people in Lahore while two months ago, an explosion in south-western Pakistan killed nearly 50 people.