Bakkali, 18, has emerged as one of the most exciting young prospects in the Eredivisie and has already been called up to Belgium's senior international squad.
He is reportedly on the radar of some of Europe's top clubs, including Arsenal and Liverpool, and PSV have been trying to tie him down to a new deal for some time.
The forward's current contract expires in the summer of 2015 and PSV have made what they feel is a generous offer for an extension.
However, nothing has yet been agreed and PSV technical manager Marcel Brands says it is up to Bakkali whether he wants to sign a new deal.
Brands told Voetbal International: "We have done all that we can.
"We have given him a good proposal and showed him a good view on the future. We won't do anything more. It is yes or no."
Reports suggest that there will be bids for Bakkali from abroad when the transfer window reopens and if he does not extend his contract then a summer departure looks likely.