A 14 month-old girl from the Sandringham Drive area of Sutton-On-Sea was taken to hospital in Grimsby, suffering from a suspected brain injury on July 28.
She was transferred to Sheffield Children's Hospital where she died from her injuries.
A 30 year-old local man has been arrested on suspicion of murder and is currently being interviewed at Skegness Police Station, Lincolnshire Police said.
More top news
Livermore looks likely to move to West Brom this week and will now hold talks with the club ahead of Saturday's game against Sunderland.
Poppy was found with diazepam, temazepam, oxazepam, ketamine, heroin, codeine and morphine in her system after suffering a cardiac arrest.
Halfback Dane Chisholm, who only signed for the Bulls from NRL side Canterbury Bulldogs in June, says he's left the club.