Flintoff, Trescothick and Giles may be rested
England will name their squad on Tuesday for the controversial one-day international tour of Zimbabwe.
But a number of the first team could be missing if they choose to withdraw.
Batsman Andrew Strauss told BBC Sport he was still undecided about whether to go or not but bowler Steve Harmison has definitely withdrawn.
Andrew Flintoff, Marcus Trescothick and Ashley Giles could also be left out when the squad is revealed by the selectors at 1430 BST.
Strauss said: "All the players have deep-rooted moral problems with going on the tour. It's not an easy situation for us to be in.
"The England and Wales Cricket Board is going to be sending out a cricket team to Zimbabwe - it's just a question of which personnel go.
"I can only speak for myself and I haven't made up my mind yet."
The ECB was in negotiations with player representatives on Monday ahead of the official announcement on Tuesday.
Vice-captain Marcus Trescothick is the only England player to commit to the tour so far.
But on Sunday, England's chairman of selectors David Graveney refuted suggestions that a stack of leading players could join Harmison in opting to give Zimbabwe a miss.
"The side will be finalised, we will consult the players and announce the squad on Tuesday," he said.
"We're going to take the strongest team - that's the way we play international
Leaving aside political considerations, England's captain Michael Vaughan and coach Duncan Fletcher believe some leading players should be rested from the tour of five one-day internationals in November and December.
Graveney did concede some players who are carrying slight injuries may be left out but insisted any fully-fit first team players were not about to follow the precedent set by paceman Harmison.
He said the tour was "subject to fitness," acknowledging a number of players such as Flintoff have been carrying injuries.
"The core players have been on the road playing constant
international cricket for a long time," he said.
"The tour of Zimbabwe gives us an opportunity to rotate a little more."
Zimbabwe have been suspended from Test cricket after the majority of their first-choice side walked out in a row over
selection policy with their national board.
The team, packed with youngsters, is struggling to compete at the top level.