The midfielder is likely to leave St Mary's this summer as Saints look to generate funds following another season in the Championship.
The Manchester City academy graduate is regarded as one of the club's most saleable players this summer, with interest continuing to grow.
However, Saints are determined not to sell below their asking price, and have already rejected two bids from Leeds as they fell below their valuation.
According to TalkSPORT, Premier League Fulham and Crystal Palace have now entered the race to sign the Northern Ireland star this summer.
EXC: Fulham and Crystal Palace have joined the race for Southampton midfielder Shea Charles. Leeds have had two bids rejected for Northern Ireland international Charles @talkSPORT
— Alex Crook ⚽️🎙 (@alex_crook) July 9, 2026
Charles enjoyed an impressive loan spell at Championship Sheffield Wednesday during 2024/25 before returning to Saints last season.
He made 38 appearances in all competitions and scored the winners in an FA Cup victory over Arsenal and a play-off semi-final against Middlesbrough.
The Elland Road club remain keen on Charles and have already had offers turned down, with Saints welcoming a potential bidding war for Charles.
The value of the latest Leeds bid was reportedly worth up to £23million plus add-ons, up from an initial £20m offer, but fell short of the club's valuation.
Reports elsewhere said Saints value Charles at around £30m, with the club also mindful that Man City are due 15 per cent of any profit made on him.