The Test series between the two nations was originally scheduled in England from June 4, but the coronavirus pandemic has put the series under doubt.
CWI chief executive Johnny Grave stated that the board has held talks with England Cricket Board regarding this matter.
Here is more.
West Indies also offered to host the Pakistan Test series
September is deemed the right time to host the series which could be hosted in the Caribbean.
It is also learnt that West Indies could also host England's Test series against Pakistan, scheduled to start on July 30.
As per the schedule, Pakistan will play three Tests in England from July 30 to August 24, followed by a three-match T20I series.
England will not lose commercial and broadcast rights
"I've spoken to Tom Harrison in the last few days and assured him that we will be as supportive as possible. Yes we have offered to host the series here in the Caribbean. The ECB would retain all commercial and broadcast rights," Grave said.
We are not trying to take any advantage, says Grave
Johnny Grave opened up about the long-standing relationship between the cricket communities in the Caribbean and England.
"This is not about us trying to take advantage of the situation," he said.
He added, "It's about the cricket community working together at a difficult time for everyone and, one of the many great things about the Caribbean is, we can play cricket all year."
Various cricket leagues have faced the wrath
On Wednesday, the UK reported 1,960 cases and 72 deaths due to COVID-19, according to the data presented by the John Hopkins University.
A number of cricket leagues around the world have been suspended, owing to the coronavirus outburst.
Pakistan Super League became the latest victim of coronavirus as the knockouts have been postponed.