Blues boss Maurizio Sarri is keen to add the 25-year-old winger but is running out of patience and time with the Brazilian. Chelsea have until next Thursday to buy players and want time to be able to switch targets if Bernard backs out.
With AC Milan and West Ham also hovering, the 14-times capped Brazil international is taking his time to decide his future having left Shakhtar Donetsk this summer.
While the Hammers are not considered much of a threat in the situation, Milan possess a cachet to their name Chelsea do not. With the club’s new owners eager to return to the Champions League, the perception is that there is more optimism to the project than at Stamford Bridge.
He hopes the move to a higher-profile league will resurrect his career with the national team. His last cap came in the humiliating 7 – 1 World Cup semi-final defeat to Germany in his hometown, Belo Horizonte.
Previously with Atletico Mineiro, Bernard spent five years in Ukraine, winning three league titles with Shakhtar.