Spanish reports claim young striker could be the first to head over to Trigoria once Enrique puts pen to paper on a coaching contract there
El Mundo Deportivo claims the 20-year-old Spaniard is keen to follow the former Barcelona B coach to the Eternal City.
Earlier, Enrique told Sky Sport Italia he has decided to take on the Roma job - and his words seem to have fuelled speculation of a cross-club transfer scheme when he said: "I want to play with the best players that I will find at Roma and some I will try to bring from Barcelona."
However, just last week Krkic said he wanted to remain at Camp Nou when his name appeared in reports linking him with a move to Villarreal as part of a supposed deal for Giuseppe Rossi.
The number nine is under contract with Barcelona until 2015, and has a reported €100 million buy-out clause.