The 18-year-old is widely regarded as one of the hottest properties in non-League football, with 14 professional clubs believed to have made enquiries for the teenager.
With 23 goals in 23 appearances for the Ryman Division One South outfit this season, the former winger has been converted into a central striker with blistering results.
Liverpool boss Brendan Rodgers was keen to take a closer look at the player, and invited Carr to Anfield to undergo a trial upon Merseyside on Thursday and Friday this week.
However, Chelsea have made a direct approach for the Dulwich Hamlet star, speaking with officials from the south London club to see about the possibility of training with the Blues.
As Chelsea and Liverpool go head-to-head for the former Reading youngster's signature, Hamlet boss Gavin Rose has hinted that he hopes to keep hold of Carr until the end of the season.
"At his age it is potential. But if he is taken by the right club and works hard he can play at the top level," said Rose. "We've got to be careful that Daniel isn't caught up in a circus. The important thing if he does go is that he goes to a club that really wants him.
"We have reinvented him. He has only played here as a striker and he is a totally different player. He has got great movement and is very clever. Daniel is decent technically, beats people on his own and scores all types of goals."