Sky Sports understands that a number of Premier League clubs are tracking the highly-rated 16-year-old.
Tanner has represented Australia at international youth level and has been with the Rovers academy for two years since arriving from his homeland. He has impressed the youth coaches at Ewood Park and this month was handed his first start for the Blackburn Under-21's, doing well in a 2-1 win over Newcastle United.
The midfielder is highly regarded at his club and it is unlikely they would welcome any approach for him. When a club has trained up and nurtured a player such as Tanner it can be hugely frustrating when bigger clubs start sniffing around. It can easily distract the player and they can have their head turned by the bigger clubs. Clearly Rovers have put a lot of time and effort into developing Hyuga so hopefully he can be allowed to progress at the club.
It is thought he could be heading for a place in the first-team squad in the not too distant future.
Blackburn are still pushing for a play-off spot under Gary Bowyer and they currently sit in 10th place, eight points off the play-offs with a game in hand on 6th-placed Nottingham Forest.
If the season did fizzle out and Blackburn had a few meaningless games at the end of the season then we could well be seeing Tanner being handed his professional debut.
Rovers already have a number of players in the first-team who have come through the youth setup at the club.
Grant Hanley, Adam Henley, Jason Lowe, and of course David Dunn all learned their trade with the club from a young age and are now established players at Ewood Park.