According to the Times' Paul Joyce, an over-reliance on Sadio Mane this season has revealed a need for added pacy wingers, and both Salah and Brandt have been identified as key targets.
Brandt has been on Liverpool's radar for some time, but Joyce added the 21-year-old German has concerns his first-team opportunities would be limited at Anfield.
Meanwhile, Salah has re-emerged as a target following former Reds manager Brendan Rodgers' pursuit of the Egypt international in 2014, per the Telegraph's Chris Bascombe.
Per Joyce, Liverpool are acutely aware they will have little chance of bagging their preferred transfer targets without being able to offer UEFA Champions League football next season.
Brandt revealed in a recent interview with FOCUS Online (via Bundesliga expert Alex Chaffer) that his prime ambition for next season is to get as much game time as possible, something that will be readily available should he stay at Bayer:
At Liverpool, Brandt would have to get used to a new league and compete for starting spots with Mane, Roberto Firmino, Philippe Coutinho and Adam Lallana.
After largely flopping at Chelsea, Salah has proved himself to be a real attacking presence in two seasons at Roma.
He has netted 27 Serie A goals and provided 16 assists for the Giallorossi in 62 appearances since the start of 2015-16, per WhoScored.com.
Salah, 24, boasts all the attributes to make him hugely effective in Jurgen Klopp's Liverpool.
He is fast, devastating on the ball and boasts excellent link-up play, while his all-round play for Roma in 2016-17 has been superb, per StatsBomb's Ted Knutson:
Liverpool started the 2016-17 season in brilliant fashion, with Mane, Firmino and Coutinho looking irresistible as a front three.
However, the trio have, unsurprisingly, endured injuries and lost form at times, and Liverpool have faded as a result.
Klopp needs to add more depth to his attack to avoid the same thing happening next season, and Salah could well be the answer.