The 71-year-old, who played "Dirty" Den Watts in the soap, is reportedly in a critical condition in the UK having returned from Bulgaria where he had been living.
According to The Sun, Grantham has been visited in hospital by close friends in the industry.
A representative for the actor asked for his privacy to be respected while a spokeswoman told The Sun: "It's true that Leslie is very poorly."
Grantham left the UK after splitting with his wife of 31 years, Jane. In 2010, he spent time in Bulgaria filming TV series The English Neighbour.
Grantham shot to fame while playing Watts in EastEnders, originally from 1985 to 1989.
A 1986 Christmas Day episode of the soap drew in an audience of more than 30 million viewers, who watched as Grantham handed over divorce papers to his on-screen wife, Angie.
The character was apparently killed off in 1989 but Grantham made a shock return to Albert Square in 2003.