The 27-year-old has been banned from football for eight months after admitting 232 separate breaches of the FA’s betting guidelines, meaning he will not play again until January at the earliest.
The news comes after Standard Sport had reported on the Blues adding Toney to their shortlist for a striker signing this summer, with the caveat that he may become unavailable should his punishment be confirmed.
Chelsea do want to sign a new striker for incoming head coach Mauricio Pochettino.
Osimhen led Napoli to the Serie A title this season, while Martinez scored on Tuesday as Inter reached the Champions League final by beating rivals AC Milan.
Romelu Lukaku is also due to return to Chelsea this summer after a season on loan at Inter. Inter have a verbal agreement to extend his loan for another season but his sizeable wages, plus a loan fee, are putting them off amid their financial problems.
Chelsea have already agreed a deal to sign RB Leipzig forward Christopher Nkunku for £53m. Nkunku primarily sees himself as a No10 but can play on the wing or up front.