The 19-year-old has impressed for Palace this season and has been linked with clubs like Spurs, Hoffenheim and Barcelona.
Liverpool believes they can land Moses for £5million, according to News of the World.
Reports says Moses would prefer staying in England and Liverpool could be leading the chase for the youngster.
Tottenham manager Harry Redknapp has claimed he needs to sell before he can buy, something that means Liverpool is in pole position to land the youngster.