The 17-year-old has enjoyed his first taste of senior football in South Wales this season, being utilised by the Swans as they navigate a difficult campaign.
Parker has featured in two Championship matches for Swansea, starting against West Midlands duo Coventry City and Birmingham City in December and January.
The attacker also earned a starting berth for the FA Cup third-round clash with League Two outfit Morecambe, providing the assist for Charlie Patino's opener in a 2-0 victory.
Unfortunately, Parker has not played a part for Luke Williams's side since the middle of January due to a troublesome hamstring injury sustained at the beginning of the calendar year.
Brighton & Hove Albion, Brentford want Swansea's Parker
According to journalist Alan Nixon, there are three Premier League clubs who are interested in securing the services of Swansea's Parker during the summer window.
The report claims that Brighton are keen on luring the Wales youth international to the South Coast, with the Seagulls having a reputation for spotting emerging talent from across the footballing world.
Roberto De Zebri's Seagulls already have a number of young wingers in their first-team ranks, including Simon Adingra and Julio Enciso.
There is also understood to be interest from Brentford, who are looking to bolster their attacking areas this summer with Ivan Toney set to move on.
Parker's current deal at Swansea expires during the summer of 2026, meaning that potential suitors would have to pay a considerable fee for his services in the summer window.
Burnley also keen on Swansea star Parker
As well as the Seagulls and the Bees, it is believed that Premier League strugglers Burnley are monitoring the development of Parker ahead of the off-season trading point.
Vincent Kompany's Clarets are fighting hard to preserve their first-tier status, with the Clarets three points behind 17th-placed Nottingham Forest with four games remaining.
Burnley's ability to battle the likes of Brighton and Brentford for Parker could be dependent on their divisional status, however the 17-year-old may have a better chance of first-team action should Kompany's troops be operating in the Championship next term.
It has been suggested that Parker has turned down an offer of a contract renewal at the Swansea.com Stadium, hinting that he could be open to a move in the summer.