Headed by the England and Wales Cricket Board's (ECB) security adviser Reg Dickason, a three-man security team recently visited Bangladesh for venue and hotel inspections, reports bdnews24.com.
Dickason was accompanied by ECB Director of Cricket Operations John Carr and Professional Cricketers Association Chief Executive David Leatherdale.
England are scheduled to play three one-days and two Tests from October 7 to November 1.
The one-day squad is due to be briefed by the team, which has returned to England, on the situation in Bangladesh on Thursday.
A militant attack on a restaurant in Dhaka on July 1 put England's Bangladesh tour under a security cloud.
Morgan, who had earlier said the tour was "a big concern", has welcomed the news that a decision is imminent.
"I'm looking forward to the meeting because it's a decision you'd prefer to get out of the way sooner rather than later or it becomes a distraction," The Guardian paper quoted Morgan as saying on Tuesday.
Test captain Alastair Cook will also be present at the meeting where information on England's last two tours of Bangladesh will be used for deeper assessment.
"They'll debrief us on exactly what the findings are from both tours and we'll get together as a side and chat about it. It has to be quite open," Morgan added.
Before the decision is made, however, Morgan pre-empted that there will be no pressure on players should the tour receive a green light from security chief Dickason.
"There's always room for a personal decision. You never put anyone under pressure to go on a tour."
The Bangladesh Cricket Board, however, described the security team's trip as a "positive" one and said there is no immediate time frame in which England were expected to make a decision.
The England one-day team will visit Bangladesh first. They are scheduled to set foot in Dhaka on September 30. The month-long tour will end with a couple of Test matches.
Before the World Twenty20 in India this year, Bangladesh hosted the Asia Cup and the under-19 World Cup without any hiccups. England were part of the latter.
After Cricket Australia had put off its national team's trip to Bangladesh for a bilateral series last year citing security concerns, the youth team also pulled out of the under-19 event for the same reason.