Liverpool face a trip to Israel after being drawn against Maccabi Haifa in the third qualifying round of the Champions League.
Arsenal will meet Lithuania's FK Ekranas or Croatia's Dinamo Zagreb as they also try to reach the group stage.
Hearts will play Greek side AEK Athens if they beat Bosnian team Siroki Brijeg in the second qualifying round.
Cork City could play AC Milan if they win their second qualifying fixture against Crvena Zvezda.
Uefa insists they will not put Liverpool players, fans and officials of Liverpool at risk as they face the prospect of travelling to the troubled Middle East.
Official Rob Faulkner explained: "We've asked the Israel FA and relevant authorities to give us assurances concerning safety."
Faulkner explained that the Israeli FA had been asked to look at alternative venues, should the game be played outside the country.
He said: "We all see the news and have serious concerns - and the situation is changing daily. But this is the right way to do it and we're asking the right people.
"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."
Maccabi president Jacob Shachar added: ""Tel Aviv is quiet - let's hope things will stay quiet and we will be able to host Liverpool.
"It's an unpleasant situation although we understand Liverpool's concerns."
Arsenal vice-chairman David Dein admitted The Gunners had set their sights on going one better than last season, when they lost in the Champions League final to Barcelona.
He said: "We want to win every competition we enter and to go that one extra step from last year. We have set our standards very high and we have to try and reach them again.
"We are also looking forward to hosting a European game at our new stadium at Ashburton Grove. I'm sure all our fans will be very proud of it because it is magnificent - one of the best in Europe."
Champions League third qualifying round draw:
Sheriff Tiraspol/Spartak Moscow v Liberec
Shakhtar Donetsk v FH Hafnarfjordur/Legia Warsaw
FC Zurich/SV Red Bull Salzburg v Valencia
Levski Sofia/Sioni Bolnisi v Chievo
Hearts/Siroki Brijeg v AEK Athens
CSKA Moscow v Djurgardens IF/SCP Ruzomberok
AC Milan v Cork/Crvena Zvezda
Galatasaray v Mlada Boleslav/Valerenga
Standard Liege v HIT Gorica/Steaua Bucuresti
Austria Magna v Benfica
FK Ekranas/Dinamo Zagreb v Arsenal
FC Copenhagen/MyPa v Ajax
Hamburg v Osasuna
FK Metalurgs/Dynamo Kiev v Fenerbahce/B36 Torshavn
Liverpool v Maccabi Haifa
Lille v Debrecen/Rabotnicki Kometal
First legs to be played on 8/9 August; second legs 22/23 August.