Scrum-half Youngs missed the Tigers' final home game of the regular season on Saturday, a 28-3 win over Bath, with a hamstring injury while fly-half Flood went off at the end of the first half with an ankle injury.
But Tigers director of rugby Cockerill thinks they will both be fit for the showdown with the team they have faced in the last two finals, winning the first and losing the second.
He said: "Ben could have played but we didn't need to take that risk. Toby, I'm not sure of the extent of his injury, I think it's an ankle. He could have carried on but there was no point in taking any risks."
Cockerill also expects two other injury victims to be fit, flanker Julian Salvi who went off early on with a leg injury, and lock George Skivington, who missed the game with a "tight back".
Leicester stayed on course for an eighth successive Premiership final with a comfortable three-try win which clinched second place, while Saracens finished third after an even better win over Exeter.
The winners of the Leicester-Saracens showdown at Welford Road next Saturday will meet the winners of the other semi-final between Harlequins and Northampton in the final at Twickenham.
Cockerill, whose team suffered a 50-point drubbing at home to Saracens at the start of the season, said: "It will be tough, and close.
"They generally are, apart from when we played at the start of the season which was 50 points.
"They have got a good record here, in fact I can't remember the last time they lost. We will have to be right on it, especially after they put 40 points on Exeter."
Ian McGeechan, who was overseeing his final game as Bath's director of rugby, tipped Leicester to win the title.
"Leicester won't be far away," he said.
"They have timed their run well and had two really good top performances at Northampton and Harlequins.
"I don't think anyone will be relishing playing them in the next round, or whatever has to come after that."
Leicester's England Saxons centre Billy Twelvetrees, who is leaving for Gloucester at the end of the season, provided the spark for the win over Bath after a poor first half which ended with the Tigers leading 3-0 courtesy of a Flood penalty.
The 23-year-old kicked 10 points and created two of the three tries, for Anthony Allen and Horacio Agulla, while the pack earned the third, a penalty try, from a scrum.
Bath's points came from an Olly Barkley penalty.
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