The 17-year-old has attracted suitors in England after a strong Scottish Cup final display and an Edinburgh derby winner in his first 14 senior appearances.
Berra, who played in England’s Premier League for Wolverhampton Wanderers, admitted that big clubs will inevitably take an interest in such a young player performing at a high level.
However, the skipper does not want the young defender to become overhyped even if he cannot ignore the speculation.
“It’s hard to ignore it. We all hear it and there isn’t much you can do about it. That stuff is part of the game now,” said Berra.
“Any young boy coming through and playing in a professional league at a good standard is going to attract attention. Bigger clubs will be sniffing because they are looking for the next big thing.
“They might buy him for a couple of million or something and then he’ll be worth £20m. That’s the way the world works. There will be teams sniffing about. They want to get the next player with potential.
“It’s all potential at the moment because Aaron has played six league games this season and the cup final last year. He has huge potential which I’m sure will make him into a good pro. He will play at a high level.
“He has done exceptionally well. However, you have to remember Harry Cochrane came in and did well and then had a tough time.
“We can’t build him up too much. Aaron has got to be level-headed, grounded, keep on learning and keep on progressing. He will make mistakes and have some ups and downs but he is doing really well just now. He is on cloud nine.
“He will have a dip because you always have dips no matter what age you are. It’s important he just gets through it and keeps on learning. He works hard in training but he is still so young.
“He has been included in the Scotland Under-19s squad and that will be a good experience for him. Getting a different type of football against different players will help his progress. It has been a really good few months for him.”