Liverpool have just completed the loan signing of Javier Manquillo from Atletico Madrid, and already have Glen Johnson and Jon Flanagan in their ranks at right-back.
Crystal Palace manager Tony Pulis hopes to make England defender Kelly his fourth summer signing after already completing deals for striker Fraizer Campbell from Cardiff, and free agents Brede Hangeland and Chris Kettings.
Kelly has struggled to establish himself in the first team at Liverpool following his return from a cruciate knee ligament injury sustained in a 2-1 Premier League defeat against Manchester United in 2012.
He returned to competitive action just over a year later but was restricted to just eight appearances for the club in all competitions last season.
The Whiston-born defender, who went on loan to Huddersfield in 2009, has played 62 times for Liverpool since being handed his first-team debut by former manager Rafael Benitez in 2008.
Comfortable playing at both right-back and centre-back, Kelly was part of the England squad for the 2012 European Championship in Poland and Ukraine, when he was called up as a replacement for Gary Cahill.
The 24-year-old has played once for England, featuring as a late substitute for Phil Jones in a 1-0 friendly win against Norway in Oslo.
Liverpool open their Premier League campaign at home to Southampton - live on Sky Sports 1HD - on Sunday at 1.30pm.