Healey's former club need to beat Wasps in the Heineken Cup final at Twickenham to add to the Guinness Premiership title and EDF Energy Cup.
"They are going like a juggernaut at the moment, almost impossible to stop," said Healey. "If they get their power game going they are literally unbeatable.
"Wasps are a physical side who will give them a run for their money but the momentum they've got and the confidence they've got means I can only see one winner.
"To win the treble would be an amazing achievement. We know the demands on players physically to go to three finals. It shows the depth of their squad.
"It's also the backroom staff who do lots of work - it shows they have everything sorted off the field."
Leicester have had to cope with the retirement of players such as Martin Johnson and Neil Back in recent years but the season where they end their trophy drought could also result in an unprecedented treble.
Speaking at the Betfair Pub Challenge, Healey added: "Leicester is the sort of club that wants to win trophies every year.
"They went five years without winning, there was a bit of the transitional period but they have been replaced with new guys making their own legacy."