The 16-year-old is seen as one of the most talented youngsters in the Eagles’ academy ranks and has been offered a scholarship by the south London club.
However, reports claim Mauricio Pochettino’s side are circling him after being impressed by the rookie.
Baptiste’s future remains unclear, with no indication given as to whether or not he’ll elect to sign on at Selhurst Park.
The teenager has been with the club since the age of 12 and already plays for their U-18 side despite his age – he made his debut in January. In February, he won the Golden Boot at the IFA Shield in India with Palace’s U-19s.
Spurs were aligned with Eagles star Wilfried Zaha before the close of the summer transfer window, who, like Baptiste, started his career in the Palace youth set-up.