Last summer Cole appeared off the bench in all three Tests for the Lions as they claimed their first series win in 16 years.
Attention now turns to New Zealand, where the Lions will head in 2017, and loosehead prop Vunipola would love to have Cole alongside him in the front row.
"He (Cole) has been key to a lot of England's success really, especially at set-piece time when he has been one of the best tightheads in the world for the last couple of years," he said.
"Davey showed that he can do a job and I think he has given the coaches confidence.
"If Dan, who is a world class prop in his own right, does go down we have got Davey who has also stepped up to the mark. He is probably pushing now for Dan to struggle to get back into the team.
"Dan Cole has been around for a long time and so has Davey and for us the more competition there is at tighthead, the better and we can only grow as a team."