Italy's Juventus, the other traditional power in Friday's draw, was paired away to Ireland's Shamrock Rovers or Bnei Yehuda of Israel, who complete a second qualifying round tie next week after drawing 1-1 in the first leg.
Both storied teams — who have been champions of Europe a combined seven times — finished seventh in their domestic leagues last season, failing to qualify for the Champions League.
For five-time European champion Liverpool, which parted with coach Rafa Benitez in May, a July 29 start in the second-tier competition represents a fall from grace.
"The disappointments of last year are well documented but it's a new era now under Roy Hodgson and it's a big tie," said club secretary Ian Silvester.
However, Liverpool's possible opponents are a mystery to the club before the return match of their second qualifying round tie next Thursday. Rabotnicki travels to Armenia with a 1-0 lead.
"If we're honest we haven't heard of the teams but we're making plans to look at the stadiums," Silvester said.
Hodgson replaced Benitez after leading Fulham to the Europa League final last season, losing to Atletico Madrid 2-1 in extra time.
The first leg at Anfield will be his first competitive match in charge, and he must prepare without a team's worth of leading players including captain Steven Gerrard, Argentina midfielder Javier Mascherano and Spain forward Fernando Torres, who sustained an adductor muscle injury during the World Cup final on Sunday.
"We're currently in a training camp (in Switzerland) minus 11 players who played in the later stages of the World Cup," Silvester said.
Liverpool and Juventus are also three-time winners of the UEFA Cup, the second-tier competition which was rebranded as the Europa League last year.
Red Star Belgrade, the 1991 European champion, also featured in Friday's draw, and will play at home first against Slovakia's Slovan Bratislava.
Turkey's Galatasaray, the 2000 UEFA Cup winner, was drawn at home to OFK Belgrade from Serbia or Torpedo Zhodino from Belarus.
IFK Gothenburg of Sweden, a two-time UEFA Cup winner in the 1980s, is away to AZ Alkmaar of the Netherlands.
First-leg matches are played July 29 and returns on Aug. 5.
Winners advance to the playoff round before progressing to the group stage.
The complex competition structure has eight teams who finish third in their Champions League groups in December join the Europa League knockout rounds in February.