Allardyce ended speculation last week, signing a new two-year contract after successfully keeping the east London club in the top flight.
West Ham could secure a top-10 finish if they beat relegated Reading on Sunday, and Collins believes Allardyce is the man to continue the club's progression.
"It is great the manager has signed his new contract, we as a team are flourishing and I know he only wants us to be getting better and better," he said.
"We are all enjoying it here. He along with all of us at the club can look to the future and plan what we want to do next in trying to take our club to the next level."
A ninth victory at Upton Park would cement a top-10 finish and set the Irons up to press on again next term.
And Collins added: "We have had a great season, to win and to finish 10th would be great.
"It is always good to finish well. In my experience if you finish one season well you normally start the next season well."