McClaren is under intense pressure as Newcastle boss as his side suffered a 3-1 home defeat to Bournemouth in a game they simply had to win in their bid for survival.
The latest disappointment leaves the Magpies in 19th position, one point behind Sunderland and safety with ten games remaining - nine for rivals Sunderland and Norwich City.
Should McClaren be relieved of his duties, Mills told BBC Radio Five Live that Nigel Pearson is the ideal candidate for the job and believes the ex-Leicester City boss may consider the post if offered.
"If there's going to be a change of manager, he needs to be an abrasive character. Nigel Pearson is available. Give him nine games, see what happens and he might take it if they give him a bonus at the end of the season for staying up,” Mills explained.
Pearson is widely regarded as abrasive and somewhat forthcoming, yet his managerial abilities can’t be questioned and there is no doubt his players always give their all under his guidance.
After guiding Leicester City to promotion via a memorable Championship campaign, he helped the Foxes preserve their Premier League status with an incredible late season run of form.
Newcastle have the players to stay up, yet they’re vastly underperforming under McClaren and on current showing they look the most likely to join Aston Villa in relegation to the Championship.
Pearson may be their best hope of survival, and in some ways they have nothing to lose by bringing him in.