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The first leg of the tie will be played at Anfield on August 8 or 9 with the second leg scheduled to be played in Israel on August 22 or 23.
Rafa Benitez, the Liverpool manager, said: "It's a crazy situation and totally unacceptable to even think about us going over there at this time.
"A few years back, when I was with Valencia, we were drawn to play Maccabi Haifa in a Uefa Cup tie and the match was switched to Cyprus. The situation then was nowhere near as bad as it is now.
"Valencia also had a European game in the Ukraine on the day the Twin Towers were attacked in America and I can remember the confusion that caused with the players on their mobile phones constantly to their families who were wondering when we'd be getting back.
"It's impossible to prepare for a game in these circumstances."
He added: "There is no way we should be going to Israel to play a game of football at this time. It's crazy to even consider it. Uefa cannot put anyone at risk.
"The situation is very clear in my mind. I feel sad for the people over there at the moment because it's a terrible time for them, but we have to put the security and safety of everyone involved before anything else and that means we cannot travel there. It would be impossible to concentrate on the game.
"Uefa need to make a decision quickly because there will be lots of our supporters wanting to know what is happening."
Rob Faulkner, a Uefa official, said: "We've asked the Israel FA and relevant authorities to give us assurances concerning safety. We all see the news and have serious concerns - and the situation is changing daily.
"We'll be in discussions with both clubs but the key is the safety of players, fans and officials - and we wouldn't go ahead if we didn't have those assurances. We have played with problems and conflict there before and also played games away from Israel. That is Plan B - a back-up plan."
Currently, Israeli teams play European home matches in the Tel Aviv area in the south of the country after Uefa lifted a ban in 2004 on matches taking place in the country. Haifa were the first Israeli team to qualify for the Champions League in 1992 and played their home matches in Nicosia, Cyprus, until the ban was lifted.
However, William Morrison, the Liverpool secretary, said the club would prefer a neutral venue for the second leg: "I don't think Cyprus is an option at the moment due to the number of people from Lebanon who are there at the moment. We'd prefer it to be played at a neutral ground somewhere else."
Les Lawson, spokesman for the Liverpool International Supporters' Club, is unhappy that Uefa have not already decreed that the tie will be moved: "Liverpool should not be even considering going there, security cannot be ensured anywhere in Israel 100 per cent and certainly not now."
Arsenal have no such security concerns after drawing the winners of either FK Ekranas, of Lithuania, or Dinamo Zagreb, of Croatia. Zagreb hold a commanding 4-1 lead going into the second leg of the second qualifying round match and are likely to be the first European visitors to the Emirates Stadium on August 22 or 23.
Heart of Midlothian will face AEK Athens, of Greece, if they can overcome Sioni Bolnisi in the second qualifying round. The Edinburgh side hold a 3-0 lead over the Bosnians and are strong favourites to progress. AEK defeated Rangers 3-0 over two legs to qualify for the group stages of the competition in the 1994-95 season.
Cork City must overcome a 1-0 deficit away to Crvena Zvezda, of Serbia, if they are to secure a mouthwatering date with AC Milan. The Serie A side were reinstated to the Champions League after their punishment for involvment in the Italian match-fixing scandal was reduced on appeal.
THIRD QUALIFYING ROUND DRAW IN FULL:
Sheriff Tiraspol or Spartak Moscow v Liberec
Shakhtar Donetsk v FH Hafnarfjordur or Legia Warsaw
FC Zurich or SV Red Bull Salzburg v Valencia
Levski Sofia or Sioni Bolnisi v Chievo
Heart of Midlothian or Siroki Brijeg v AEK Athens
CSKA Moscow v Djurgardens IF or SCP Ruzomberok
AC Milan v Cork City or Crvena Zvezda
Galatasaray v Mlada Boleslav or Valerenga
Standard Liege v HIT Gorica or Steaua Bucuresti
Austria Magna v Benfica
FK Ekranas or Dinamo Zagreb v Arsenal
FC Copenhagen or MyPa v Ajax
Hamburg v Osasuna
FK Metalurgs or Dynamo Kiev v Fenerbahce or B36 Torshavn
Liverpool v Maccabi Haifa
Lille v Debrecen or Rabotnicki Kometal
Ties to be played on 8/9 and 22/23 August
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