Ralph, who plays for FA Cup hopefuls Woking, is out of contract at the end of this season and it is claimed the Surrey side would prefer to cash in, in January.
The 24-year-old was previously on the books of Peterborough United, Yeovil Town and Newport County, and is said to want to return to the Football League as soon as possible, which may give the upper hand to either Charlton and Oxford United.
Indeed, Charlton's relationship with Woking - to whom they have loaned a number of players down the years, including Regan Charles-Cook this season - is sure to be considered by the Cardinals.
Nevertheless, a move to Hearts, who compete in Scotland's top flight, may be seen as an appealing option to Ralph.
The Essex-born player, who stands at six feet tall, can also play higher up the left flank if required.
Can Charlton, Oxford United, Hearts or anyone else win the race for Ralph?