The Sky Sports report comes after Floyd Schofield pulled out of this weekend's world title fight after being deemed "too ill" to challenge Stevenson for the WBC lightweight belt.
Leaked messages, reportedly from Schofield's dad, Floyd Schofield Sr, accused unnamed people of poisoning his son.
Padley, 29, has a record of 15 wins including a stunning upset over Mark Chamberlain in his last fight on the undercard of Anthony Joshua vs Daniel Dubois in September.
The move came after a rumour spread on social media that Schofield had been "poisoned" before he failed to show up among the arrivals on Tuesday night.
UNBEATEN Josh Padley is set to be parachuted in to fight Shakur Stevenson this weekend.
