The Premier League club are interested in acquiring the services of the winger, claims The Irish Independent, who also mention Celtic as potential suitors.
The 18-year-old has made 18 appearances and provided four assists for Cork City in the Irish top flight in 2025.
It was previously reported that O'Sullivan was set to join Crystal Palace, but The Irish Independent says there is a 'strong possibility' the teenager will wait until the end of the Irish season to leave Cork, which coincides with the end of his contract.
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The winger could come up against Celtic next Tuesday when Brendan Rodgers' side travel to Cork for their second pre-season friendly.
The Scottish Premiership champions begin their preparations for the new campaign with a game against Queen's Park on Friday night.
Manager Brendan Rodgers said [CelticTV]: "When you're a big club, they're never friendlies.
"But certainly they give us a great time to prepare when we have some of these really good games.
"But then you add into that the qualification for Champions League, then of course that means that you're trying to get to the end point that little bit quicker because it's something that's very, very important to us.
"So, yeah, we take that last qualification leg when it comes, and hopefully we'll be in a really good place by that time."