PSV winger Gakpo is a man in demand heading into the final hours of the transfer window, with Leeds United and Southampton heading the queue.
Southampton have agreed a fee for the winger, along with personal terms, but PSV have yet to sign off on the switch.
A potential complication has now emerged as Chelsea have made a move for Sangare, according to Dutch daily the Eindhovens Dagblad.
Chelsea have indicated they are prepared to pay between €40m and €45m to sign the midfielder.
Sangare is open to the move to Stamford Bridge, but PSV will not sell both him and Gakpo on Thursday.
It remains to be seen which of the two deals might go through and whether PSV could be offered enough money to convince them to change their stance and sell both.
PSV have potentially tough decisions to make on Thursday as they deal with serious English interest in their crown jewels.