The Claret Jug awarded to the winner of the Open Championship is traditionally engraved as soon as the outcome is known, unlike the silverware Rose collected for his maiden major triumph at Merion last month.
"I'm hoping I'll get a two-for-one deal this year, because I think he's going to engrave the US Open trophy for me," Rose said of engraver Garry Harvey, who took over from his father in 2004.
"The big difference between the US Open and The Open Championship is that you get the trophy with your name on it at the prize ceremony. With the US Open you get it done yourself. So I'm hoping I get a discount for bulk!
"I've pretty much carried the trophy around for most of the last month. Just being able to share it with friends and family and people that have known me since I was 12 years old, and now they're getting a chance to have a picture with the US Open trophy or be able to have dinner and have it sitting on the table. Just little moments amongst close friends and family, that's what really makes it special."
The odds are stacked against Rose winning on Sunday, with only six of the greatest players ever having won the US Open and Open in the same year.
But that will not stop the 32-year-old Englishman from trying to emulate Bobby Jones (twice), Gene Sarazen, Ben Hogan, Lee Trevino, Tom Watson and Tiger Woods.
"The Open Championship as a British player is the one event you look forward to more than any other all year," Rose added.
"And coming in here off the back of my first major makes it even more special, I guess even more exciting than normal.
"I'm looking forward to getting to play again. I've had three weeks off, the idea being to get my legs back under me, to get 100 percent ready to play again.
"And I feel that's been the case. I've spent the last couple of weeks just with family and getting my hunger back for wanting to get back out on the range.
"The challenge for me is going to be staying in this tournament, not being dragged back to Merion every five minutes."
Rose's best result in the Open remains his remarkable share of fourth place as a 17-year-old amateur at Birkdale in 1998, after which he turned professional and missed 21 cuts in succession.
"If you look at my results, they're really not very good in this tournament," added Rose, who played nine holes in practice on Wednesday with Nick Faldo, twice a winner of the Open at Muirfield.
"But I would say that the reality is a little bit better than that.
"I felt that in 2009 at Turnberry I had a good chance to win there. Just nothing really went my way on Sunday and I putted poorly for the most part on that day (he finished 13th). In 2002 here I was tied third going into the last round.
"Obviously I was just a little bit young and needed a lot more experience under my belt, but given that sort of similar situation this year, that's a situation I'd once again relish.
"I do feel comfortable on links golf. I think having grown up having played so much of it in the amateur game, you know how to play it.
"The yardage book means very little this week and I think only experience can really help you through that. I see no reason why I shouldn't do well here."