The United States international has been linked with a potential move to the Premier League over the past few seasons.
Liverpool FC are thought to be interested in a deal to sign the American playmaker given his past working relationship with Jurgen Klopp.
Manchester United have been listed as another potential destination for Pulisic over the past 12 months.
Chelsea FC are planning for life without Eden Hazard and Willian given the duo are attracting interest from FC Barcelona and Real Madrid.
However, ESPN FC pundit Mariner believes Pulisic would be foolish to leave Dortmund for Chelsea FC if Hazard and Willian remain at Stamford Bridge.
“I hope he doesn’t go to Chelsea,” Mariner told ESPN FC.
“Unless they sell Hazard or Willian, he will never get into the side.
“If he does, can he replace Hazard or Willian? Absolutely not at the moment.”
Chelsea FC appointed former Napoli head coach Maurizio Sarri as their new manager last month after Antonio Conte was sacked.
The Blues made Italy international Jorginho their first summer signing in a £57m deal from Serie A giants Napoli.
The west London side signed former England international Rob Green in a free transfer to provide cover in goal.
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