The Hammers' vice-chairman Karren Brady sparked controversy at the weekend when she said the Premier League should be declared "null and void" after its suspension in the wake of Covid-19.
Brady received criticism for her opinion because it would be a solution which would suit the London club, given they are out of the relegation zone on goal difference.
But Cole, who played for the Hammers over two spells, reckons they would have no problems when, or if, the campaign restarts because of David Moyes.
"West Ham were on the back of four great performances I thought, I watched them closely," he told the PA news agency.
"The break has come and when the restart comes whenever it does, it will be about who starts better.
"When you come back and the season restarts, if it does, having an experienced manager who knows how to organise a team and David has a lot of experience doing that.
"West Ham will benefit from that. We don't know what will go on the other side of things but from football point of view it will give them a chance to get some players fit. But everyone else will be thinking the same."
The situation might become clearer on Thursday as Premier League clubs meet to discuss possible outcomes to the current campaign.
Whatever is decided, there seems no possibility of a quick resumption given the increasing cases of coronavirus and the prediction that they may not peak for several weeks.
The Hammers currently find themselves in 16th place in the Premier League table with Moyes' side suffering a 1-0 defeat to Arsenal in their last outing before the imposed break.