That is according to pundit and former MLS footballer Alejandro Moreno, who says there is a reason why Aubameyang has not left Borussia Dortmund yet.
Chelsea are in the market for a striker after manager Antonio Conte told Costa he can leave the club this summer as he was not in his plans for the upcoming campaign.
The Blues wanted to re-sign Romelu Lukaku from Everton but they have seemingly lost out to Manchester United, who announced this morning they had agreed a fee with the Toffees for the Belgian.
Aubameyang is one of three forwards from across Europe who are linked with Chelsea, with Real Madrid's Alvaro Morata and Torino's Andrea Belotti other options.
ESPN
Alejandro Moreno says Chelsea should not sign Pierre-Emerick Aubameyang
There is a reason as to why so many people have walked away from Aubameyang
Alejandro Moreno on Borussia Dortmund striker Pierre-Emerick Aubameyang
Aubameyang's move to French side Paris Saint-Germain collapsed earlier in the transfer window despite him telling Dortmund he wants to leave.
Moreno says the fact Klopp, who managed the Gabon international for two years in Germany, has not tried to sign him at Liverpool should put Chelsea off.
"There is a reason as to why so many people have walked away from Aubameyang," ex-Venezuela international Moreno said on ESPN FC.
ESPN
Alejandro Moreno says not even Liverpool want to sign Aubameyang so Chelsea shouldn't
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"He seemed to be the hot property and somehow he kind of fell off the radar, PSG doesn't want him anymore, and this team doesn't want him anymore.
"Even a guy like Jurgen Klopp who had him at Borussia Dortmund, there is no conversation of that going on.
"So if people who have worked with him are saying 'we don't want him' there's got to be something else that we are not privy too, so I don't want him either."