The 19-year-old's father won five of his seven world titles with the Italian team from 2000-04, helping transform Ferrari into the most successful team in Formula One after more than two decades without a drivers' championship.
Mick Schumacher is currently second in the Formula Three European Championship and is being closely monitored by several F1 teams after winning six of his last 10 races.
"Concerning Mick Schumacher I think the most important thing is to let him grow, without giving pressure," Arrivabene told reporters at the Singapore Grand Prix on Friday.
"Recent results are very, very good and I wish him a great career. With a name like this, that wrote historical pages of Ferrari history, the door of Maranello is always open.
"(But)... that is a family decision, I mean a Schumacher family decision. Let the guy have fun. I always repeat this -- be focussed, concentrated, but in the meantime have fun, and to grow slowly, but certainly, and then we'll see about the future.
"How can you can say 'no' at Maranello to a name like this?"
Haas team principal Guenther Steiner felt it was too early to make a call on the young driver without knowing what his future plans were, while Sauber's Frederic Vasseur added that it was a huge step up from Formula Three.
"With the small number of test days we have in the winter, I think it's -- I don't want to say impossible -- quite difficult to do the step and it will make sense probably for him to do Formula Two or something like this," Vasseur said.
"But he could have a link with a Formula One team, he could do some (race weekend practice sessions). There are many ways to prepare for F1."
McLaren sporting director Gil de Ferran said he had not had any contact with Schumacher but would like to be able to help talented drivers like him progress in the sport.
"We are always looking throughout the motor sport arena globally, in a way," De Ferran said.
"I wish we had more opportunities to be able to work with young talent, perhaps more testing and different things like this, to be able to establish a relationship and help in the development of drivers like Mick."
(Reporting by John O'Brien; Editing by Christian Radnedge)
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