Cole hopes West Ham hold onto Allardyce
Allardyce's contract is up at the end of the season and negotiations on a new deal are not expected to get underway until survival is secure.
"Sam has done a great job and has been fantastic with me," said the 31-year-old midfielder.
"He has an unbelievable record as a manager, is an experienced manager and you see what he is about on a daily basis. What a great manager he is.
"We want to stick another two or three wins on the board and I am sure that will be much more than enough (to secure survival).
"The gaffer came in when the club was in a bad state and has done a phenomenal job.
"The owners have done a great job backing him and the lads, the players, have done a great job to come up. It is very difficult to do that.
"We can't rest on our laurels now. We've got to constantly move forward and try to win every game."