Reports linking him to the Potteries have gathered momentum north of the border over the past week.
O’Neill, a huge admirer of the Scottish market, is also an admirer of Boyle, but Stoke won’t be so keen on an apparent £1m valuation for the 27 year-old wide man.
Stoke are adequately stocked with recognised wingers at the moment in the shape of Tom Ince and James McClean, while there is also the prospect of young Belgian Thibaud Verlinden returning next season from a cruciate knee ligament injury sustained on February 12.
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O’Neill has also been prepared to play the likes of Nick Powell and Tyrese Campbell out wide, but may want a more natural winger to supplement or even replace the personnel he has.
Stoke will consider the touted £1m asking price steep in the present financial climate for a player unproven outside Scotland and who has only one year left on his current contract at Hibs.
A more structured deal based on appearances and team and individual success would be more to the club’s liking were Stoke to pursue this one.
Much of the impetus for the Boyle speculation may be prompted by his representatives, but it also appears that Hibs are keen to do business with someone to boost their troubled finances.
The club has asked players to take wage cuts on top of wage deferrals in the wake of the coronavirus pandemic, while the prospects of money-saving job cuts could reportedly stretch as far as first-team coach Grant Murray.
Boyle himself has spoken freely in the past about the attraction of playing in England.
He has previously said: “I’ve seen players at Hibs flourish over the years and didn’t see why that couldn’t be me.
“I saw boys move on to bigger and better things, the likes of John McGinn, and it just shows you what can be done if you keep your head down and continue to work hard.”
O’Neill, meanwhile, has been up front about his roving eye when it comes to Scottish players – and that admission has helped fuel speculation linking him with half-a-dozen names north of the border.
O’Neill, whose family home is in Edinburgh, believes there is a pool of young and hungry talent with plenty of first-team experience under their belts because of the shape of Scottish football.
But 27 year-old Boyle might not be encouraged by O’Neill’s statement in April that: “We wouldn’t typically be looking at players who’ve been in Scottish football for a long time because we don’t see them as having the right profile for the kind of player we’d like.
“But certainly the younger ones are worth considering.”