Stuart Lancaster's men are building towards the 2015 World Cup on home soil and are set to face the elite of rugby union later this year, with New Zealand, South Africa, Samoa and Australia all due to visit Twickenham.
They will do so without Cole and Vunipola, however, after their respective Aviva Premiership sides ruled them out of contention.
Cole, who has undergone surgery on a neck issue, is not set to return to action for Leicester Tigers until at least November.
Speaking at the Aviva Premiership launch, Tigers director of Rugby Richard Cockerill said: "Coley has had the all-clear from the surgeon to ramp up his training and that was a week ago.
"He should be fit about 12 weeks from that date, so we're hoping Dan will be playing again in 10 or 11 weeks, but we will see.
"We will give him as much time as he needs. The disc that has been replaced will be stronger than the one he had in there in the first place.
"It's far more important that he gets his neck absolutely right rather than come back a bit early and have issues with it. Stuart Lancaster is very sensible about it. Coley will be ready to play when the specialist deems he is ready and not before."
Vunipola, who also plays prop, is still recovering from a knee injury sustained in Saracens' defeat to Toulon in May's Heineken Cup final and too is unlikely to be playing again before November.
Saracens director of rugby Mark McCall stated: "Mako has an injury from the European final. He’ll be out for a while - until November possibly. But he has no chance for the autumn internationals.”