"There's false news doing the rounds," he told a news conference in Glasgow on the eve of Tuesday's Champions League tie at Celtic.
"It's completely untrue that five players showed up late for training. I'd like to know who is starting these stories."
The Gazzetta dello Sport newspaper suggested that strikers Mario Balotelli and Robinho were among the five latecomers.
Allegri also refuted the idea that it was a relief for Milan to play away from their San Siro stadium where they received an angry reaction from fans after Saturday's 1-1 draw with Genoa, their seventh game in all competitions without a win.
"The team shouldn't be thinking about what happens outside the changing room," said Allegri who, according to media speculation, is clinging to his job.
"Of course there's bitterness and disappointment among the fans. We feel it too and so does everyone who works for the club.
"We have to do everything we can to do better and to do that we need to have the fans with us. It's not true that it's better to play away from the San Siro - it's always better for us to play at home in front of our fans."
Milan (five points) are second behind Barcelona (10) in Group H, one point ahead of Ajax Amsterdam and two clear of Celtic.
Allegri is hoping a good run in the Champions League can deflect attention from his team's dismal showing in Serie A where they are 13th.
"We have to separate the league from the Champions League," he said. "We have to get a result tomorrow as the second objective of the season is to get into the last 16.
"The first objective was to qualify."
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