Sky Blues boss Micky Adams has been linked with moves for Rangers man Nacho Novo and Lillestrom's Michael Mifsud after having a bid of around £800,000 turned down for McKenzie.
Now it is believed that Coventry have bid closer to £1million, and the Canaries may be willing to sell the 28-year-old, despite having so far failed to add any more bodies to last season's squad except midfielder Lee Croft.