Vunipola, who has 34 England caps, limped off in Saracens' comprehensive 41-13 victory over Sale Sharks on Saturday and there were immediate doubts over his fitness with the international fixtures just around the corner.
It has now been confirmed the 24-year-old has been removed from the Red Rose's training squad although there is still a chance he will be back to full fitness in time for the matches in November.
Harlequins ace Clifford, who can play across the back row, has been added to the squad and he will be hoping to make an impression as he aims to add to his seven caps.
The Brisbane-born star, who is also 24, has made three domestic appearances so far this season - against London Irish, Gloucester and Wasps - although he has yet to open his account for the campaign.
England's first autumn international is against Argentina on November 11 before clashes with Australia and Samoa later that month.