The highly-rated 19-year-old has long been linked with a move away from Selhurst Park, with Manchester United, West Ham and Newcastle amongst those reportedly interested in the right-back.
However, Clyne is set to leave Palace for newly-promoted Southampton, with reports suggesting he will pen a four-year contract at St Mary's.
It is understood a deal has not yet been signed, although the club is confident of completing a move for the full-back within the next 24 hours.
Clyne broke into the Palace first-team at the beginning of the 2008/09 season, making his debut in a 3-0 home win over Barnsley.
He penned a three-year deal soon after and grew to become one of the Eagles' key players.
Clyne won the club's player of the year award for the 2010/11 season and last term was included in the npower Championship team of the year.
The defender is out of contract at Palace, who will be due compensation for the academy graduate as he is under the age of 24. If a fee cannot be agreed between the clubs, it would go to a tribunal.
Source: PA
Source: PA