The Gunners have showed a strong interest in the England international, though they face competition from other Premier League clubs.
However, Leicester are reluctant to sell one of their key players ahead of the 2021-22 campaign, which will see them compete in the Europa League once again.
Arsenal were also keen to sign Maddison 12 months ago, and the Daily Mail claims that they had a massive offer rejected by the Foxes.
It is suggested that City will take a similar transfer stance this window, meaning that Arsenal - or any other interested sides - may have to table more than £70m.
Maddison played a direct part in 13 Premier League goals last season, despite injuries restricting him to 24 starts.