The England U-21 goalkeeper enjoyed an impressive spell at Carrow Road last season. He played all 46 matches in the Championship and appeared in five domestic cup games.
The report claims that the final fee could rise to around £15 million, although it is not clear whether City have a buy-back clause for the 22-year-old goalkeeper.
Gunn is a very talented keeper and is tipped as a future England international. However, he would have to struggle to get regular games at City especially due to the success of Ederson.
The news will come as a blow to Leeds United who were heavily interested in signing him.
The Whites are looking to sign a top quality goalkeeper but but haven’t been able to lure any of their targets so far.
It remains to be seen how Leeds approach their goalkeeping issue, but with Gunn now off the radar, they are increasingly likely to move for Jamal Blackman.