Robinson had previously been on trial at Goodison Park, where he impressed Toffees boss Roberto Martinez, and negotiations are ongoing regarding the future of the former St Kevin's Boys youth player.
The 18-year-old, who has featured for the Irish First Division side on three occasions this season, was recently included in Paul Doolin's Republic of Ireland squad for the upcoming Under-19s Championships Elite qualifying round.
|5/1||Everton are 5/1 with William Hill to finish in the Premier League top four next season|
"Everton are chipping away with us on Ryan at the moment and we hope to get the deal over the line soon," he told the Irish Examiner.
"The initial fee won't make us millionaires but we'll make sure it's heavy on the end of it. It might be better for us to go for the add-ons and everything else."
He added: "Ryan certainly has a big future in the game. Everton would have seen a rawness to him but he has a lot going for him.
"We'd have no problem allowing him to move on to a better level in England."
The Toffees have had success in importing from Ireland before, with Seamus Coleman signed from Sligo Rovers in 2009 and going on to be named in the PFA Team of the Year for his performances in 2013-14.