The 22-year-old inspired Gloucester to victory at London Welsh yesterday, having rescued them from defeat at Worcester and tallied 25 points at London Irish.
Burns was sensational in Sunday's third win of the season as he created both Gloucester's first-half tries and was the starting point for their third late on as they moved up to fifth in the Aviva Premiership table.
And now Davies, who has coached the likes of Lions fly-half Stephen Jones and Wales 10 Rhys Priestland, reckons Burns will star on the big stage if England coach Stuart Lancaster gives him a chance this year.
"I've worked with a lot of international 10s and Freddie's right up there," said Davies.
"He's playing exceptionally well. A game like this can be very difficult for you if you don't get it right at No10. But for large parts he controlled the game, put us in the right areas and was a constant threat.
"As a 10 it's not all about you: it's about how you manage the team and run the team, and he's really starting to do that.
"The fact that he has been able to mature at this level for a couple of years has certainly helped him.
"His goal kicking is improving all the time and his game management and out of hand kicking is excellent at the moment."
Burns produced back-to-back moments of brilliance to deal the Premiership newcomers a double blow in the first period and he then rescued Gloucester from the jaws of defeat with time running out.
The youngster raced from one 22 to the other on the 15-minute mark, forcing Welsh wing Nick Scott into a deliberate knock on, before his quick tap penalty saw Shane Monahan dive over.
His sniping run then provided the momentum for Tom Savage to power through on the half hour and Gloucester were good value for an 18-9 lead at the break.
It was a very different story for Gloucester after the interval as the Exiles hit back to lead 25-21 but Burns was at it again to save his side with eight minute left.
The England Saxons star, who isn't in Lancaster's EPS squad, ran from the shadow of his own posts to spark a move that eventually saw replacement prop Shaun Knight dummy over for the winner.