The Gills, who secured promotion in March, will be crowned champions if they secure at least a draw when they face AFC Wimbledon at the Priestfield Stadium on Saturday.
Allen told BBC Radio Kent: "To be promoted was very, very special for me but to be the manager of the champions would be great.
"I thought we would do well right from the beginning but it has been remarkable.
"It would be very special to everybody - the supporters, the players the staff and myself - and a great day in all our lives."
Gillingham are six points clear at the top of League Two.