The transfer window for Premier League clubs has already closed, but remains open in a host of other European leagues until August 31, AFP reported.
Hazard's Belgian teammate Thibaut Courtois forced a move from Chelsea to Madrid earlier this month by refusing to return for preseason training after helping his country finish third at the World Cup.
After starring himself in Russia, Hazard seemed to suggest his time at Stamford Bridge was coming to an end, saying his "preferred destination" was well-known.
But after coming off the bench to inspire a 3-2 win over Arsenal on Saturday, Hazard remained coy over whether he will remain at Chelsea beyond this season.
"Leaving this year? I will not leave," he told French radio station RMC.
"Many things have been said. A lot of it nonsense. For now, I'm happy. I still have two years of contract and we will see what happens.
"We can sell but we cannot sign players. It would be a bit odd for them to let me go and not recruit a player after."