Hodgson has presided over just one away league win this season
The head of the body that represents football managers in England has warned that clubs should not be "treated as the playthings of the super rich".
The jobs of Roy Hodgson at Liverpool, Gerard Houllier at Aston Villa, Carlo Ancelotti at Chelsea and Avram Grant at West Ham are all reportedly at risk.
League Managers Association chief executive Richard Bevan has urged clubs to stop "scapegoating" their managers.
And he suggested it might time for managers to undergo formal appraisals.
Bevan wrote: "In these, the strengths and weaknesses of how the football-side of the club is performing might be assessed against realistic expectations and previously, mutually agreed goals.
"In any other sector, there is a recognition that the highest performing organizations are those who build winning organizational culture - shared beliefs, goals and ways of behaving - coupled with a long-term vision.
"Yet, in football, there is an incomprehensible belief that the continued sacrificing of the football manager, the 'scapegoat' and installing another will turn around a football club's performance."
Nineteen of the 29 managers to have parted company with their clubs this season have been sacked, while 21 coaches have also been dismissed following managerial departures.
Those figures are slightly down on this time last year when 33 managers had departed by the end of the first week of January in 2010.
"They actually serve to highlight the continued chronic short-termism in football manager employment," Bevan added.
The LMA chief executive cited academic research showing that the effect of changing managers initially brought an average 2.5 points for Premier League clubs, before a team's performance dipped backed to a level below that achieved before the managerial switch.
"It is clearly the decision of club chairmen whom they hire and fire and when they choose to do this," Bevan continued.
"But the statistics show that a club is likely to end up worse off when they sack their manager, they have less points and are often significantly out of pocket due to monies spent on compensation and paying up contracts.
"Clubs in lower leagues simply cannot afford to keep sacking managers."
A manager's average tenure during the 2009-10 campaign was one year and four months, compared to three and a half years in 1992, according to Bevan.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.