The series would follow England's visit to the West Indies from January to April of next year and provide a final tuneup ahead of the 2009 Ashes, when holders Australia visit England starting in July.
England's invitation, which the West Indies Cricket Board (WICB) said remains under discussion, would be for the Caribbean side to play two Test matches and three one-days.
Dr. Donald Peters, Chief Executive Officer of the WICB, said a decision would be made in the coming weeks.
"The WICB has a request to play two Tests and three ODIs in England. We are examining all possibilities," he said.
"At this stage it presents some challenges because the West Indies will be hosting a series - including Tests and One-Day Internationals - against Bangladesh in early May next year," Dr. Peters said.
Accepting the invitation would mean juggling Bangladesh's scheduled visit as part of the International Cricket Council (ICC) plan that has such tests planned seven years in advance.
England's tour of the West Indies remains on schedule as planned, Peters said.
"They (England) want to play us twice in one year," he said.
Sri Lanka pulled out of its scheduled England tour because most of the nation's players will be involved in the Indian Premier League (IPL).
"We are still talking," Peters said, careful to consider Bangladesh tour plans for the Caribbean.
"If we accept the invitation we would have to determine how best we could work out the logistics and planning issues."
England's team is set to arrive for training in the Caribbean on January 21 in Barbados and play Tests in February and March in Jamaica, Antigua, Barbados and Trinidad and Tobago before five one-days.