The omission of O'Driscoll - the squad's most senior player - for the third and final Test has been heavily criticised, with head coach Warren Gatland instead opting for Davies and Jamie Roberts. It is a significant vote of confidence for Davies, who moves to his more accustomed position of outside centre to accommodate Roberts' return.
"I wouldn't say I feel any extra pressure, I'm just grateful for the opportunity to play in such a big game. Brian is one of the greats because of what he's achieved," Davies said.
"I was very grateful to him for coming up and congratulating me. Everyone who isn't involved on Saturday has shown a professional attitude. That's been one of the positives of the tour. Brian is like everyone else, he came up and congratulated me. We've got on with training since.
"I was obviously over the moon to be involved in such a massive game. Training has gone really well this week and the boys are looking forward to it. It's a huge task and we're really focused on the task in hand. I was glad to get the nod and looking forward to taking my opportunity again.
"Personally I'm pretty pleased with the way I've been playing, but I need to make sure I deliver on Saturday."
Gatland stressed that he used his "head not his heart" when deciding the make-up of his midfield, but discarding O'Driscoll remains one of the great selection shocks in Lions history.
Roberts, fit again having recovered from a hamstring strain nearly three weeks ago, will forge his familiar Wales centre partnership with Davies.
"Jamie has a big, physical presence and gets over that gainline," Davies said. "He's done extremely well over the last couple of weeks to get back fit.
"To have someone like that come in shows the strength of the squad. It benefits that I've played a fair bit with him at country level. What he brings is something different and I'm looking forward to playing with him again. It's an exciting prospect."