Koeman took over at Southampton at the start of the campaign and he has guided them through an impressive season.
Southampton are currently in fifth place in the Premier League table and Allardyce paid tribute to the job that Koeman has overseen earlier today.
"Ronald Koeman probably [deserves to win the award] for what he’s done at Southampton in his first year and with the number of players they’ve changed around," he said. "They managed to sustain a top sixth position which is a fabulous achievement."
Koeman had an unenviable task when he took over at St. Mary's, but he has done brilliantly in his first season in England.
Southampton had appeared to be in trouble after losing a number of their key players last summer, but Koeman steadied the ship and purchased well.
It means that the Saints appear stronger now than they did even last term, and Koeman's achievements could still deliver even greater rewards.
Southampton are only five points off the Champions League qualification spots at present and, with Manchester City in such poor form, they will feel they have a chance of bridging that gap before the end of the season.