Rose, the 2013 champion, was reluctant to get too far ahead of himself but acknowledged how much it would mean to add a second U.S. Open title at the most famous course on the rotation.
"There's a long way to go," he said. "And yet here and St. Andrews would probably be the two most iconic places to lift a bit of silver.
"I couldn't think of anything better. But if you don't mind I'm just going to wait a couple of days."
Rose is ranked fourth in the world but he arrived to little fanfare at Pebble Beach, where the focus of pre-championship attention was very much on Tiger Woods and two-times defending champion Brooks Koepka.
Top of the world rankings as recently as February, Rose went missing in the first two majors of the year, missing the cut at the Masters before finishing equal 29rd at the PGA Championship.
The 38-year-old Englishman is too good to go missing in action for long, though, and it was no surprise to find him atop the leaderboard after his second round on Friday.
Playing in front of a huge gallery with Woods and Jordan Spieth, Rose was methodical rather than brilliant.
After enjoying the putting round of his life to take the first-round lead with a six-under-par 65, he could not quite run the tables on the greens again but did enough to compile a no-nonsense 70.
Rose spoke about the importance of "hanging around" within striking distance of the lead, and not pressing too hard until the right opportunity presented itself.
"My short game has been really, really strong this week," he said.
"I've made a lot of putts inside ten feet. I've managed my game really well. I've missed it in the wrong spots. I've always given myself an opportunity to salvage something out of every hole I've played. And I haven't compounded any mistakes so far."
(Reporting by Steve Keating; Writing by Andrew Both in Cary, North Carolina, editing by Nick Mulvenney)
