The 18-year-old defender only made his League of Ireland debut last week but has already been called-up to the Ireland Under-19s squad and may well be on the move in the next few weeks.
Everton famously paid just £60,000 to Sligo Rovers for Seamus Coleman in 2009, the player later going on to become one of the finest full-backs in the Premier League and picking up the club's 2013/14 Player of the Season Award.
Speaking to the Irish Examiner, Shelbourne manager Johnny McDonnell confirmed that negotiations were at an advanced stage with Everton over a deal to sign Robinson.
However, wary of what happened with Coleman it seems Shelbourne are keen to guarantee future revenue by ensuring any deal will include additional payments linked to appearances.
"Everton are chipping away with us on Ryan at the moment and we hope to get the deal over the line soon.
"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.
"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."