Abraham - who spent the season on loan at relegated Swansea City - was heavily linked with a move to St James's Park last summer.
And now the Sun are reporting that Benitez is once again eyeing up a move for the tricky frontman once again as he prepares to return to parent club Chelsea.
The 20-year-old netted eight times in 40 appearances for the Swans last season, and also picked up a first senior international cap as Gareth Southgate called him off the bench to feature in England's friendly against Brazil.
Meanwhile, the Mirror report that Newcastle are battling it out with Premier League rivals West Ham for Reims goalkeeper Edouard Mendy.
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The Guinea-Bissau international enjoyed a productive season in Ligue 1 and, with a reported asking price of just £2million, he is expected to attract plenty of interest.
West Ham are thought to be favourites as Manuel Pellegrini hunts for a new stopper, but the report suggests that Benitez also has eyes on the 25-year-old.
It's still all quiet at Sunderland, as Stewart Donald nears a managerial appointment.Here's the rest of the news hitting the back pages today:
Manchester Unitedare closing in on the signing of Brazilian Fred from Shaktar Donetsk (Manchester Evening News)
Defender Toby Alderweireld is also interesting Untied - but Spurs want £75million for the Belgian centre back (Mirror)
Leicester City are holding out for a £60million fee for Riyad Mahrez as Manchester City try to snap up the Algerian after narrowly missing out in January (Guardian)
Former Chelsea midfielder Michael Ballack could return to the club as Director of Football (Evening Standard)
Spurs have joined the race to sign Ahmed Hegazi from recently-relegated West Brom (ESPN)
Everton defender Leighton Baines has no desire to leave the club despite reports linking him to LA Galaxy (Liverpool Echo)
Zenit St Petersburg boss Maurizio Sarri has yet to agree a new contract with the Russian side, as he is keen on a move to Chelsea (Mail)