The former England international has been in and out of the team at Leicester City and has struggled to adapt to life after leaving Wolves, which was perhaps the peak of his career.
Rangers have held talks with the 32-year-old in recent weeks, which have looked promising, but now, according to the Daily Mail, Wrexham have entered the race for him.
Co-owners Ryan Reynolds and Rob McElhenney have signalled that they do not plan to stay in the Championship for long with their business so far this summer, and Coady, who has extensive top-flight experience, seems to be top of their transfer wishlist as they try to boost their squad to the next level.
The Welsh side have already broken their club transfer record twice this summer, first for Empoli left back Liberato Cacace and secondly for Nottingham Forest midfielder Lewis O’Brien.
They are also ready to break that record once more after agreeing a £7.5 million club record move with Ipswich Town for forward Nathan Broadhead.
Coady is in the final year of his contract at the King Power Stadium and has made 198 Premier League appearances so far in his career.
If he dodges a move up to Glasgow to join Rangers, however, he may find himself featuring in the Premier League once more if he can help Wrexham get promoted in what would be another fairytale season.