The Sun says Liverpool and Newcastle United are tracking the 21 year-old midfielder.
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Newcastle are hoping to have an edge given the success of fellow Brazilians Bruno Guimaraes and Joelinton under manager Eddie Howe.
Newcastle are ready to make a move for Allan, with an opening £40m offer being prepared.
Napoli had a bid of £34m recently rejected with Palmeiras anticipating a major auction for the summer market.
Allan's deal with Palmeiras runs to 2029.