Mario Balotelli, signed by the Anfield side for £16 million this summer, is reportedly already considered in some circles to have been a gamble that backfired.
Berahino, meanwhile, is not only the best-scoring Englishman in the Premier League, he is now the third-top scorer in the top flight overall with seven goals to his name.
And the Reds want to bring the Baggies striker to Merseyside in January, claim the Mail. But there are two problems...
First of all, there is the not so avoidable stumbling block that Tottenham Hotspur are also said to be extremely interested in signing the 21-year-old. Like Liverpool, Spurs' front men are yet to consistently find the back of the net this term.
Harry Kane has impressed for the north London side in the Europa League but neither he, nor Emmanuel Adebayor or Roberto Soldado have imposed themselves in the Premier League. Berahino is thus said to be a prime target for Mauricio Pochettino.
A second issue also exists in that West Brom will not sell the striker for less than £25 million, according to the report. And is such a fee really wise when Liverpool have already spent so much this summer - with most of their signings so far failing to look good value?
But these, of course, could all still just be rumours.