The 28-year-old, who has made 21 appearances for his Italian club this season, has a contract in Naples until the end of the 2022-23 campaign.
According to Corriere del Mezzogiorno, Everton, having been linked with the midfielder in January, have now launched a £17m offer for the South American.
However, the report claims that the Serie A side are looking for twice as much as the Toffees are currently offering, while interest from Paris Saint-Germain could see his valuation rise again.
Allan - capped on eight occasions by the Brazilian national team - has contributed one goal and one assist in 14 Serie A appearances this season.
Everton are currently eighth in the Premier League table, just five points behind fourth-placed Chelsea, who will welcome Manchester United to Stamford Bridge on Monday night. body check tags ::