The 71-year-old, who played iconic character Den Watts in the BBC soap, had been living in Bulgaria but has reportedly returned to the United Kingdom for hospital treatment.
A rep for Leslie is quoted as telling the publication: "It's true that Leslie is very poorly".
His agent said a statement would be issued "at the appropriate time".
Leslie's character in the BBC soap EastEnders, Den Watts, made headlines over the years.
Infamous for their arguments, the couple adopted Sharon, who Den famously referred to as "princess".
Grantham's character was later shot and killed by criminal gang "The Firm", departing the show in 1989, however soap bosses resurrected the character in 2003 for one of the show's most shocking storylines.
After two more years of wreaking havoc on Albert Square, Watts finally met his maker, as his three ex-girlfriends united to kill him, burying him under his beloved Queen Vic pub.
A former soldier, Grantham learned to act while serving a 10-year prison sentence for the murder of a German taxi driver while on army service.
Grantham was also the subject of a 2004 tabloid newspaper sting, when he was exposed masturbating on live webcam and sucking his finger in his dressing room.
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