The 20-year old has been included in a potential deal which would see he and Thiago depart the Nou Camp for Arsenal in exchange for Cesc Fabregas and around £25million.
"Luis Enrique and Bojan know each other and so he would certainly like to come to Roma," Vekic told Il Corriere dello Sport.
"It would be a perfect marriage, but we have to wait. We have to be careful because the decision is down to Barcelona.
"The player's father would prefer not to speak with anyone. He works for Barcelona and he does not want things to become confused, so he has ordered total silence."