The non-League sensation has been in scintillating form for the side from south London this season, scoring 23 goals in 23 games in the Ryman League Division One South.
Reds boss Brendan Rodgers wants to invite Carr to Merseyside to take a closer look at his credentials for Premier League football, with the talented teenager currently playing eight divisions below the top-flight.
Anfield scouts have been impressed with Carr's performances for Dulwich Hamlet this season, and are believed to have already made a number of trips to Champion Hill.
Hamlet boss Gavin Rose will be keen to keep his leading scorer at the club until the end of the campaign, but admitted in an interview earlier this season that he will be perilous to prevent any player leaving for a bigger club in the summer.
"We'd like to hold onto our boys to give us the best chance of competing in the league, which is so tight," Rose explained. "If someone comes in for them at the end of the season then we would give them our blessing as a club.
"It's the normal attention from clubs but we're trying not to focus on that and concentrate instead on the boy progressing."