An injury will keep Ascot winner Subjectivist out of the Group One race (July 27, 3.35pm) so John and Thady Gosden's seven-year-old is now the leading selection.
Stradivarius has already won the race four times, more than any other horse, but Gosden would have loved to have taken on his Ascot conqueror again.
"He's been in good order since Royal Ascot. The Gold Cup was a fascinating race and Subjectivist put in a superb performance," he said.
"I'd love to have got in a race with the winner, but we never had the opportunity to get there and that's life.
"I think Frankie (Dettori), having ridden him so brilliantly in previous Gold Cups, seemed to have a brainstorm and sit 12 lengths of the pace!
"I'm sorry that Subjectivist is not able to run next week, it's heartbreaking for everyone involved and it would have been great to have enjoyed a 'Duel on the Downs'."
Having lost one stable star to retirement in Enable last season, Gosden is thankful to owner Bjorn Nielsen for keeping Stradivarius in training as long as he has.
"He's very much part of family here - we had Enable with us until she was a six-year-old and him until he is seven. It doesn't normally happen with full horses like him," said Gosden.
"Everyone enjoys his company, and he checks everything in and out from his box and he knows Clarehaven inside and out. He enjoys going out on the Heath and shouting at the other strings!"
Mark Johnston's Sir Ron Priestley was a supplementary entry for the contest after his victory over Al Aasy in the Princess Of Wales's Tattersalls Stakes at Newmarket in June taking the number of possibles to 13.
The five-year-old bounced back from two successive losses to win at Newmarket and will now be one of two Johnston runners alongside Nayef Road.
Sir Ron Priestley was defeated in the Yorkshire Cup Stakes by Andrew Balding's Spanish Mission and the two are likely to meet again.
Spanish Mission followed up his Knavesmire victory with a third-placed run in the Gold Cup at Ascot, a performance that saw him finish ahead of several Goodwood Cup rivals.
Amongst them were the Aidan O'Brien-trained trio of Santiago, Serpentine and Amhran Na Bhfiann, who finished seventh, eighth and 11th respectively.
Only the latter has run since, triumphing in a Group Two at the Curragh by seven lengths.
O'Brien has two further entrants in the race, with King Of The Castle also engaged alongside Passion, who was third behind Amhran Na Bhfiann in the Curragh Cup.
Emperor Of The Sun holds an entry for O'Brien's youngest son Donnacha, with Alan King's Champions Day winner Trueshan also engaged.
Jamie Osborne's Mekong and Ismail Mohammed's Away He Goes complete the list.
A setback ruled five-year-old Ocean Wind out of the race.
Trainer Roger Teal said: "He's had a bit of a setback, so he's going to miss Goodwood.
"We are just monitoring him and checking him, and (will) then see what we do for the rest of the season.
"It's not very serious, but we just need to give him a bit of time. It's not bad, but we just have to monitor the situation at the moment.
"It's very disappointing - we've come so close."