The Frenchman was hampered by injuries in the recent campaign, but he was still impressive with 10 goals and six assists from 19 games.
He currently has a release clause worth £60 million in his contract and reports claim that Palace are preparing for his potential departure.
United have been credited with an interest alongside the Blues, but Academy Scoop claim that they are fearful of missing out on him.
Joe Shields, who is Chelsea’s co-director of recruitment and talent, has a good relationship with Olise from his time as a Manchester City junior.
This could potentially give the Blues the advantage over the Red Devils.
Chelsea failed with an approach for Olise last summer and the board are determined to secure his services this time around.
The arrival of Olise could pave the way for the departure of Noni Madueke as the Blues need to balance their books due to PSR limits.
