West Ham are struggling in the Premier League this season and are in 18th place in the league table with 20 points from 23 matches.
Moyes is under pressure as the Hammers have managed to pick up only one win from their last eleven games.
However, Cunningham stated that the West Ham hierarchy will not remove Moyes from the Hammers managerial role because of his experience.
The former Republic of Ireland international also believes that Moyes, with a track record of dealing with relegation battles, is the right person to guide the team in their situation.
“They are very reluctant in these situations to pull the trap door so I think David Moyes is safe and just in terms of experience which he has on his track record”, Cunningham said on Off The Ball.
“I think there is a stat mentioned about his number of wins in Premiership but with his general experience and being in this position, it’s not as if he is a manager who has been constantly competing at the top end of the table.
“He has been in this position before, so I think he is probably the one best serve to get them out of this situation.
“Yes, a little bit of pressure to an extent that I can understand, but I see him there between now and the end of the season.”
West Ham will welcome Nottingham Forest on Saturday to the London Stadium before they face Manchester United in an FA Cup clash on 1st March.
