Andrew Flintoff and Steve Harmison have been identified by England coach Peter Moores as having doubts over returning to India after the Mumbai attacks.
"Fred has had issues and it's fair to say Steve Harmison has as well," said Moores, as England wait for a security report to determine if they will tour.
"The important message from me is that we respect people and allow them to have their views," added Moores.
"The key is we get clear information. I hope as a team we all go together."
England have set up a training camp in Abu Dhabi while they wait to discover if the two-Test series will go ahead.
Senior England officials have travelled to India to assess security at Chennai, where the first Test is due to start on Thursday 11 December.
Hopefully we can take our full-strength side there, compete, win the series and have a good Christmas
Hugh Morris, managing director of England cricket, and Sean Morris, chief executive of the Professional Cricketers' Association, will return to Abu Dhabi on Sunday with their conclusions and an announcement on the tour is expected shortly afterwards.
"What I do know about those two guys is that they are massively proud to play for their country and both have missed out on Test match cricket and are both desperate to play again," said Moores.
"It's not as though they have been on the road for 18 months and are desperate for a break. If any player like that didn't go it would hurt him as much sat at home as any of the other players.
"Freddie quite rightly wants to take all the information in and make his call.
"If he thinks it's right he will go and represent his country. If he thinks he can't, that will be a tough decision for him, and it will be his decision."
England's training schedule in Abu Dhabi was interrupted by bad weather and led to the cancellation of Saturday morning nets.
"Mentally, everyone has to assume we are going." said Moores. "It's about getting your skills ready to go as a batter or a bowler.
"It's such a quick turnaround now, so the lads have got to get themselves together really quickly if they are going to be ready."
ENGLAND'S TOUR OF INDIA
First Test Chennai, 11-14 December
Second Test Mohali, 19-23 December
"There's a general will within the team to go and play these Test matches," added Moores.
"Because, one, people will be representing their country but also in the situation in which we find ourselves after what happened in Mumbai.
"But everyone will have different opinions and if someone doesn't want to go we will respect that.
"Hopefully we can take our full-strength side there, compete, win the series and have a good Christmas."
International Cricket Council (ICC) president David Morgan believes playing the Tests could send out an important political message.
"I believe the Test series will be a clear demonstration of the resilience of the Indian people and the game of cricket and an illustration that the game has the ability to bring people together," said Morgan, a former chairman of the England and Wales Cricket Board.
The England team went home last Saturday following the attacks in Mumbai, which claimed almost 200 lives over three days.
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