Ferrari's door will always be open to Mick Schumacher, says its Formula 1 team principal Maurizio Arrivabene, but there are no plans for an affiliation yet.
Schumacher has moved to within three points of Red Bull junior Dan Ticktum for the Formula 3 European Championship lead thanks to six wins in the last three rounds, including a clean sweep of the recent Nurburgring triple-header.
His father Michael won five of his seven F1 titles with Ferrari, and 72 of his record 91 grand prix wins, while racing for it from 1996-2006, and stayed affiliated with Maranello until making his F1 comeback with Mercedes in 2010.
Arrivabene stressed it was crucial not to put 19-year-old Mick Schumacher under too much pressure yet.
"The most important thing is to let him grow, without giving pressure," he said.
"The recent results are very, very good, and I wish to him a great career.
"With a name like this, that wrote historical pages of Ferrari history, the door of Maranello is always open, of course. But without burning the step.
"That is a family decision, I mean a Schumacher family decision.
"But let the guys have fun. I always repeat this: be focused, concentrated, but in the meantime have fun, and 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?"
Schumacher, whose father Michael has not been seen in public since being badly injured in a skiing accident in late 2013, is not currently officially affiliated to an F1 team.
He is supported by Mercedes in F3 and drove the manufacturer's DTM 'taxi' at the Nurburgring last weekend alongside his racing commitments.
Schumacher is expected to move to Formula 2 next season, but is also poised to end 2018 with enough points this season to qualify for F1's mandatory superlicence.
Drivers need 40 points over a three-year period and Schumacher already has 22, so he will be eligible for an F1 licence if he finishes in the top three in European F3 - 30 points are awarded to the champion, 25 to the runner-up and 20 to third place.
Schumacher earned 10 points for each of his second-place finishes in the 2016 German and Italian Formula 4 Championships.
He also received two for finishing second in the 2014 CIK-FIA World Karting Championships in the KF Junior category, and points earned in karting are valid for five years.
Sauber team principal Fred Vasseur advised against a leap straight to F1.
"Honestly I think there is a huge step between the F3 and the F1," he said.
"With the small number of test days we have during the winter, it's - I don't want to say impossible - but it's quite difficult to do the step, and it would make sense probably for him to do F2.
"But he could have a link with an F1 team, he could do some FP1s. There are many ways to prepare for F1."