"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, Strauss said.
"I can only speak for myself and I haven't made up my mind yet."
Earlier Sunday, chairman of selectors David Graveney insisted that injuries will not be used as a smokescreen to leave players out of the controversial tour of Zimbabwe in November.
The England and Wales Cricket Board (ECB) have assured players they will not face reprisals if they opt out of the five-match one-day tour like paceman Harmison on moral grounds.
But Graveney said that they remain committed to sending a full-strength squad, and will not be using injuries as an excuse to leave certain players out of the tour. "The side has not been selected. We will finalise our squad today," Graveney told BBC Radio Five Live's Sportsweek programme.
"Steve Harmison is the only player who has indicated he is not going to Zimbabwe. We will then announce the squad on Tuesday. In my period of being a selector we have always selected the strongest side. The only question with any team is subject to fitness."
"A lot of players have been carrying a number of injuries during the summer and it will be up to the medical staff to inform the selectors if a period of rest would be beneficial for the demanding programme they have ahead of them." Graveney said.
"We're not trying to conceal anything. These guys, particularly the core players who play both Tests and one-day internationals, have been playing constant international cricket for a very long time."
"We're going to take the strongest team. That's the way we play international cricket but we'll take the fitness angle into account. The selectors were castigated for taking injured players to Australia and we're very conscious of that," he added.