Pulev is the mandatory challenger for the IBF belt and Joshua has until December 2 to face him.
And Pulev says the fight is now booked for next month.
“Anthony Joshua is a great and dangerous rival, but his style fits perfectly with mine,” the 36-year-old Pulev, who has only one loss in 26 fights, wrote on his page in Facebook on Monday.
“In boxing, the boxers’ styles dictate the match and there’ll be not many hugs, there will be a heavy boxing (on Oct 28).
“My preparations go very intensely because of the short time I have, and I will be perfectly ready when I get into the ring so that he has no chance against me.”
The 27-year-old Briton, undefeated in 19 fights, had been due to face Wladimir Klitschko in a rematch of their April bout, which Joshua won with an 11th-round knockout, but Klitschko has since announced his retirement.
Pulev, one of Bulgaria’s most popular sportsmen, turned professional at the age of 28 in September 2009, less than a year after winning the European amateur boxing title in Liverpool.
He has held the European heavyweight title twice between 2012 and 2016 and has challenged once for the unified world heavyweight title in 2014, losing to Klitschko in Hamburg on a fifth-round knockout.
