Pulisic has struggled to make his mark at Stamford Bridge due to injuries and is thought to be on the Blaugrana's radar for a possible move in 2022.
The Blues would supposedly sanction a sale for £42.5m in straight cash, but El Nacional claims that a swap deal involving De Jong could also be on the cards.
The former Ajax man - who has also been linked with Manchester City and Manchester United - does not see his deal at Barcelona expire until 2026.
Pulisic, meanwhile, has just under three years left to run on his deal with Chelsea, and the 23-year-old has two goals from six appearances in all tournaments this term. body check tags ::