Reports also indicate that the team may travel via the Middle East on Thursday and play a warm-up match in Abu Dhabi itself.
However, speaking to a radio channel on Tuesday, former England bowler Dominic Cork said that he expected "five or six" players not to return. "They are upset and feel they wouldnt be able to go out," he said. "Those Ive spoken to are traumatised. What they saw on television was 10 times worse than what was shown here. I am not sure about the captain. I know of players who are going to put their families first."
England selectors, it is believed, have short-listed three Middlesex bowlers - Tim Murtagh, Alan Richardson and Steven Finn - as stand-byes, should the trio of Andrew Flintoff, Steve Harmison and possibly James Anderson decide not to travel.
But Cork also believes that if any of the playing staff do not want to tour on safety grounds, the tour should be called off. "If one doesnt go, they all shouldnt go. They should make a stand and say 'It's not safe for us to be there."
England's security expert in Chennai
Englands one-day squad returned home last Saturday after the final two internationals were cancelled in wake of recent Mumbai terror attacks which left almost 200 dead.
Meanwhile, the Board of Control for Cricket in India has, on its part, shifted the Test venues to Chennai and Mohali, from Ahmedabad and Mumbai. But it now seems that the team's security adviser will be seeking an upgrade to a protection level that was already high.
England and Wales Cricket Board's security expert Reg Dickason arrived here this morning to make a recce of the stadium and hotel and discuss with officials the security arrangements.
Dickason is believed to have involved the need for a blanket security from the National Security Guards (NSG), the same special forces who stormed the Taj Mahal Palace hotel last week. There are also unconfirmed reports the ECB has asked for commandos to accompany the team at all times, an emergency evacuation plan and total security around dressing rooms.
After Chennai, he will then proceed to Mohali, the venue of the second cricket Test, and undertake a similar exercise.