Allofs worked alongside Schaaf for over 13 years before accepting an offer from Bundesliga rivals Wolfsburg last November.
Since he left, the club have slumped to the edge of the relegation places and, with five games of the season remaining, they are just five points above the bottom three.
Schaaf is quickly losing support as he approaches his 14-year anniversary in the job, a date which falls just a week before the end of the season, but Allofs remains convinced that he should be allowed to celebrate that milestone in the Bremen hot seat.
"Werder simply could not wish for a better coach in terms of his identification with the club and the work he does every day in all areas," he said.
Whether Schaaf then has a future beyond the end of a season, or whether the club should start anew, will depend on the long-serving coach, according to Allofs.
"In the end, Thomas has got to take that decision," he told the Weser Kurier newspaper.
"He has got to decide for himself to what extent he feels he can realise his ambitions."