The Reds, who only qualified for the competition by virtue of winning last season's Carling Cup, were seeded in Group Two and could have been paired with Dundee United for clashes that are set to be played on August 2 and 9.
But the three-time winners instead await the winners of a second qualifying round clash, with Gomel taking a 2-0 lead into the second leg next Thursday.
Gomel, who play at the Central Stadion, are managed by Oleg Kubarev and finished third in the Belarusian Premier League last year, while Renova were fourth in the Macedonian First League.
Rodgers will be looking to make an immediate impact in his first two matches in charge - with the domestic campaign getting under way a little over a week after the Reds play their second leg clash.
Success in the Premier League will be paramount after Liverpool finished eighth last season but Rodgers has already spoken about setting high standards from the off.
The Reds were seeded on Friday alongside Dinamo Moscow, Steaua Bucharest, Bursaspor, the winners of Young Boys v Zimbru Chisinau and Mura 05 v CSKA Sofia.
They could also have faced Ukrainian side FC Arsenal Kyiv or the winners of NK Osijek v Kalmar FF, FC Spartak Trnava v Sligo Rovers and Maccabi Netanya FC v KuPS Kuopio.
Liverpool are currently on a pre-season tour of North America and will play their first pre-season game against Toronto on Saturday.