Garnacho has only been a first-team player for Man United since last April, but the 18-year-old has featured on 36 occasions for the senior side, scoring five goals and registering five assists in the process.
The Argentina international was handed a new long-term contract by the Red Devils towards the end of last season, which he finished with five goals and five assists in 34 appearances.
Garnacho missed a chunk of football in the second half of the campaign due to an ankle injury, but he made a goalscoring return against Wolverhampton Wanderers last month.
The teenager currently wears the number 49 shirt for the Red Devils, but according to the Manchester Evening News, the club are considering handing him arguably their most famous shirt.
The report claims that the number seven jersey is being discussed internally as a possible option for the South American to reflect his status at Old Trafford.
The '7' has been available since Cristiano Ronaldo's departure at the end of last year, and should Garnacho be handed the shirt, he would become the first teenage recipient of the jersey since Ronaldo in 2003.
Eric Cantona, Bryan Robson and David Beckham are among the legendary figures to previously sport the number, while Michael Owen, Antonio Valencia, Angel Di Maria, Memphis Depay, Alexis Sanchez and Edinson Cavani have also worn it in recent years.
Garnacho made the move to Old Trafford from Atletico Madrid in 2020, and he has now fully established himself in the first team at Old Trafford.
Ten Hag said towards the end of last season that the Argentine's main challenge was to now secure a regular starting role at the club, having been primarily used off the bench in the early stages of his career.
"One of the aspects for the biggest talent is that they are mature. First, they take responsibility and second, they are mature. To bring in the skills, they have belief that they can dominate opponents. And once again he did it," said Ten Hag.
"He had a big impact in many games either when he's starting or coming on. He's ready, straight into the game and that is so important for the squad that you can bring young players and I'm happy you can bring young players. Hopefully, he can progress so quickly he can compete for a starting XI position because that is his next challenge.
"He is showing when you score some winners - Fulham - the assist against [Manchester] City and now the second goal, he is showing some things. Also sometimes he lacks defensive transition and pressing.
"He has to step up, when you are going into an action or keep the ball, so decisions. But when you see all over he is a huge talent and he is brave."
Garnacho is currently on his post-season break but will be back in pre-season training with Man United at the start of July to prepare for the 2023-24 campaign.