James Rodriguez and Allan are set for Everton medicals while the Merseyside club are also trying to sign Abdoulaye Doucoure.
Sky Sports are reporting that the Colombian playmaker Rodriguez and the Napoli midfielder are both set to have their medicals on Wednesday.
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Rodriguez will join the Toffees for an undisclosed fee on a three-year deal which will see him play under Italian manager Carlo Ancelotti for the third time in his career. The 29-year-old made just 14 appearances for Real Madrid in all competitions last season.
Napoli president Aurelio De Laurentiis confirmed Allan said his goodbyes in Naples at the weekend and was pictured landing in Liverpool in a private jet on Wednesday afternoon.
The 29-year-old is expected to complete his move of around £25m at the same time as James.
The Watford Observer say talks are continuing between Everton and Watford over midfielder Abdoulaye Doucoure with reports late on Wednesday suggesting that a fee had been agreed.
The 27-year-old midfielder looks set to leave the relegated Premier League club with AS Monaco and Fulham also believed to be interested in the Frenchman.
Analysis: Ancelotti is making his mark
Allan and Rodriguez are both set for moves to Merseyside as Ancelotti builds a side that he, and all Everton fans, will hope can do a whole lot better than finish 12th.
Everton made seven permanent signings in the 2019/20 summer transfer window and arguably only one of those, Andre Gomes, really improved the quality of the starting XI.
They required a smarter transfer strategy entering into this window and, although a few weeks ago reports emerged of an unhappy Ancelotti - there must have been a lot of loveable eyebrow raising going on - at the lack of transfers being made, it appears the Toffees are getting their act together.
Allan and Rodriguez enter the wealthy club with vast top-flight experience and boast Champions League pedigree. The experienced duo could forge one of the most exciting midfield pairings in the Premier League while Doucoure would be a very promising addition, too.
It is unlikely Everton could attract Allan and/or Rodriguez to Merseyside if Ancelotti was not the manager. The Italian has worked with both players before. If the 61-year-old can squeeze the best out of his former Real and Bayern player Rodriguez, 29, in particular, then Everton could be a real force in the fight for European places this season.
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