Bought by Godolphin in the off-season, Profitable has been ultra-consistent this term, finishing second in France, at Royal Ascot and Glorious Goodwood.
Priceless followed in Profitable's hoof prints by winning the Temple Stakes at Haydock, but she has been some way behind her stablemate the last twice.
Both need to find some improvement seemingly, to trouble ante-post favourites Lady Aurelia and Battaash.
"At the moment both Profitable and Priceless are intended runners in the Nunthorpe," said Cox.
"Both seem in good form at home and deserve to take their chance. The long-range forecast looks decent and this would be in both their favour.
"Profitable ran well at Goodwood – we were very happy with him. He has come out of the race in good form.
"It looks like being a very competitive race – certainly a mouthwatering contest – and one that will be great to be part of.
"It is always great to have runners at York – especially in the big races. Everyone wants to be part of it. It is a great occasion and somewhere we love to have winners."