McClaren has lost left backs Ashley Cole and Wayne Bridge for the game on March 24 to suspension and injury, while striker Peter Crouch is also out.
There could be more injury woes as the weekend Premier League games are followed by Monday's FA Cup quarter-final replays. Manchester United face Middlesbrough and Chelsea take on Tottenham Hotspur.
More than half the 23-man squad McClaren is due to name on Friday will play in the replays, exposing England's already flagging campaign to more damage.
McClaren, whose side are third in Group E, may even have to plunder the Under-21 squad if things go awry up front.
England are expected to start with Wayne Rooney and Andy Johnson at the Ramat Gan stadium, with Jermain Defoe and Darren Bent on the bench.
Should any of them suffer injury by Tuesday, McClaren would have to look to the likes of Preston North End's David Nugent, a second division player, as emergency cover.
England's qualifying campaign, which continues against Andorra in Barcelona on March 28, has at least been lifted by the return at club level of Lennon and Hargreaves.
Lennon, though usually on the right for Spurs, looks set for the problem left midfield role for England, with the other flank given to Steven Gerrard.
LEFT PROBLEMS
"It's been well-documented that it's been a problem area since Joe Cole had his injury," McClaren told reporters.
"But we've got options there, we've seen Aaron Lennon, who can play right side, left side and at the head of a diamond.
"He came into the World Cup and excited us from day one, played a cameo part in some games and we expected to see a lot more of him this season.
"Unfortunately, because of injury and illness we haven't seen him as much as we'd like."
Hargreaves, back with Bayern Munich after a broken leg, will return to the holding midfielder's role, freeing up Frank Lampard to attack Israel's rearguard.
"We saw the importance and emergence of him in the World Cup. He was a catalyst," McClaren said.
"He allowed Gerrard and Lampard more freedom to express themselves and I think we've missed that since he's been injured."
With Ashley Cole back for the Andorra game, McClaren said he would choose between Jamie Carragher and Phil Neville as his replacement to face Israel.
Liverpool's Carragher looks the favourite, given the eulogy from McClaren for his "fantastic performances against Manchester United and Barcelona.
"For me, he is one of the unsung heroes of their club, someone every team needs, someone who very quietly, very professionally gets on with their job; great character."
That character will be needed by the likes of Carragher and captain John Terry, who made his Chelsea comeback in midweek at Manchester City after being concussed in their League Cup final win over Arsenal.
"This is a big game, an important game, and I believe it's a game for experience," said McClaren.
"It's that English aggression, backs-against-the-wall kind of performance that we need.
"John Terry epitomises that, that's why I picked him as captain. To have him out there would be a massive boost to us."
Unfazed by England's prospects, McClaren added: "We've been in this situation many times before.
"We've had bad results, doubts about qualification, and when their backs are against the wall, that's when the big players have to step forward."
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