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Vunipola, who now has eight England caps, will come into consideration for Saracens' European quarter-final against Ulster this weekend however.
But Saracens director of rugby Mark McCall is insistent that Vunipola will not be rushed back before he is ready.
"Billy has a chance, probably a bit more than 50 per cent, and has been training with us this past few days," said McCall, a former Ulster coach.
"We'll make a decision later in the week. If Billy plays it'll be because he's fit to play. We won't take a risk with any player."