The England and Wales Cricket Board (ECB) earlier said it sought government instruction on the tour following a terrorist attack on the Holey Artisan Bakery in Gulshan -- the diplomatic heart of the Bangladeshi capital -- a hangout for foreigners and the well-to-do, on Friday night.
The ECB is seeking the counsel and guidance of its director of security, Reg Dickason, on whether the tour will go ahead as planned with England scheduled to reach Dhaka on September 30 for the month-long tour.
"It is quite a big concern. We've always left the big decisions to the ECB," Morgan was quoted as saying by bdnews24.com on Tuesday.
"They write reports and send guys out to see if it is safe and then come back to the players to see how happy or unhappy they are. Certainly it is a concern at the moment."
The militant violence developed into a hostage crisis, a first in Bangladesh, leaving at least 22 persons dead in its wake -- among them an Indian, nine Italians and seven Japanese.
In 2008, England were playing a series in India which was hit by the Mumbai terrorist attacks. The touring team flew back home from India due to safety concerns, but later returned to play two Tests in Chennai and Mohali.
Morgan thought "it could be feasible" if the series was relocated to a neutral country.
Bangladesh Cricket Board President Nazmul Hossain remains hopeful that the series would continue, drawing hope from the ongoing Euro Championship in France -- which came under coordinated attacks about seven months ago.
"There is no way cricket can escape the consequences (of the attack). England's reaction is natural. If I was in their position, I would've done the same," he said on Sunday.
"Although Paris came under attack the games weren't put off. I believe sport will move on in its own pace," Hassan added.