The Reds have already signed Joel Matip, Loris Karius and Marko Grujic in deals totalling less than £10m as Jurgen Klopp looks to rejuvenate his Liverpool squad.
The 18-time English champions were thought to be keen on Bayern Munich forward Mario Gotze but the £20m transfer target has reportedly committed to the Bundesliga champions.
According to a report in the Portuguese media, Liverpool are very close to completing a £45m deal for Brahimi, which would make the Algeria international their record signing.
Andy Carroll is still Liverpool’s club-record purchase after his £35m switch to the Reds from Newcastle United in January 2011, while Brendan Rodgers signed Christian Benteke in a £32.5m deal from Aston Villa last summer.
Liverpool lost 3-1 to reigning champions Sevilla in the Europa League final in Basel last week.
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