Ireland's Champion National Hunt trainer likes sending his dual-purpose performers over for the big staying handicaps in Britain and nearly pulled off a notable double with Thomas Hobson at Royal Ascot last week.
So far the Pitmen's Derby has eluded him, but he appeared to have an ideal candidate in Ivan Grozny, a winner at Galway on his last Flat outing who handled the all-weather in France and is owned by a north-east native in Graham Wylie.
However, his participation now looks unlikely.
"I'm not sure if he's going to go you know, he'd have nearly top weight which wouldn't make it easy," said Mullins.
"Also, I just haven't been 100 per cent happy with him lately so he's probably not going to run, I'd say."
Ivan Grozny was a low as 12-1 for the extended two-mile handicap, which is worth nearly £100,000 to the winner.
Globetrotting stablemate Wicklow Brave is set for a weekend outing, with Mullins eyeing the Comer Group International Curragh Cup.
Having beaten Order Of St George in the Irish St Leger last year, he went on to run in the Melbourne Cup.
Although that did not go to plan, he showed the fire burns as brightly as ever when winning the Punchestown Champion Hurdle under a terrific ride from assistant trainer Patrick Mullins.
He was last in action in America when a fast-finishing fourth in the Belmont Gold Cup.
"I'm very happy with Wicklow Brave at the minute and as we stand I'd say he's going to run at the weekend," said Mullins.
The likes of Frontiersman and Forgotten Rules are possible opponents on Sunday.
