Ireland midfielder had previously been linked with Leicester
Everton are believed to have entered the race for Robbie Brady's signature.
The versatile Norwich City midfielder shone at Euro 2016, with suggestions that Premier League champions were keen on acquiring his services.
But reports have linked new Everton manager Ronald Koeman with a move for the Dubliner.
The Sun are claiming that the Toffees have now overtaken Leicester on the list of clubs aiming to bring him back to the Premier League.