The Feyenoord forward, 15, is able to move to a different club in December when he turns 16 and the two Premier League giants are interested in his signature.
According to The Sun, Chong has already been at Old Trafford for talks and Louis van Gaal is confident of completing a deal. However, Chelsea are preparing to swoop in at the last-minute in an attempt to take him to Stamford Bridge.
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The youngster has been a part of Feyenoord's academy since 2009 and currently plies his trade for the Under-17s.
The current Premier League champions have one of the best academy set-ups in world football and their academy team won the UEFA Youth Cup last season.
However, the vast majority of players fail to make the grade and the Blues have not produced a first-team regular since John Terry.
The club are trying to change that fact and English midfielder Ruben Loftus-Cheek is slowly making his way into the setup under Jose Mourinho.
The Stamford Bridge club also have the likes of Patrick Bamford, Dominic Solanke and Nathan Ake among their 33 loaned out players.
Manchester United have also struggled to produce first-team regulars in recent years. However, James Wilson, Andreas Pereira and Patrick McNair are knocking on the door at Old Trafford.
Despite spending an eye-watering amount of money since taking over at the Red Devils, Van Gaal is famed for giving youth a chance and is trying to integrate academy graduates into the fold at United.
Chong has a big decision ahead of him with both clubs keen on his signature, and the next couple of months will have a huge impact on his future.
In terms of first-team appearances, his best option could be to stay at Feyenoord, but the allure of the Premier League giants may be too good to turn down.
What should Tahith Chong do: go to Manchester or Chelsea or stay at Feyenoord? Have your say below!