Defence coach Alex Sanderson revealed during an interview with BT Sport that Vunipola - who also missed the British and Irish Lions tour of New Zealand with a shoulder injury a year ago - "can't feel his wrist", raising further questions over whether he will play a part in England's Six Nations campaign.
Eddie Jones is due to name his squad for the championship on Thursday, but faces a big selection headache in the days leading up to the announcement. The no.8 reeled away clutching his right wrist after it banged into Ospreys' Rob McCusker as the Saracen tried to make a tackle in the 38th minute.
Jones is already without injured backrowers Nathan Hughes - Vunipola's regular understudy - and Tom Curry while flanker James Haskell faces a disciplinary hearing this week after a red card for a late shoulder charge to Jamie Roberts' head in the Wasps-Harlequins game at the weekend.
"Billy is due to see a specialist later this week, when a timeframe for recovery may be defined", said a Saracens spokesman.More news: United open to January transfers amid Sanchez rumours
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Having undergone an X-ray on Sunday, Saracens confirmed that Vunipola had suffered the broken arm, which represents his fourth major injury in 14 months and could result in a fourth surgery depending on the outcome of a specialist appointment later this week once the swelling has gone down.
The luckless Vunipola had earlier given a strong indication that he was facing another frustrating period out of the game. "You know me, never one to do anything subtly". I thought I did that better this time.
He will also be sorely missed by European champions Sarries, who are in great danger of missing out on the Champions Cup quarter-finals after they were held by the Ospreys.