Both London clubs wanted to sign Barkley during the summer, and the midfielder reportedly rejected a £35m move to Stamford Bridge on the final dayof the window.
The 23-year-old, currently out until December with a hamstring injury, is out of contract at Goodison Park in the summer, meaning he will be available on a free transfer, so both Tottenham and Chelsea will look to sign him in January for a reduced price of £20m, according to the aforementioned source.
The fact that Barkley rejected Chelsea in the summer suggests that he may favour a move to Mauricio Pochettino's Tottenham, where the Argentinian coach has established an English core to his team with players such as Harry Kane, Dele Alli and Eric Dier.
Barkley came through the youth ranks at Everton but his career at the Merseyside club looks to be over after he reportedly turned down a new deal worth around £100,000 per week and Everton boss Ronald Koeman said in the summer that he would not play again for him.