Both colts are owned by Sheikh Hamdan bin Mohammed Al Maktoum.
Dee Ex Bee finished second in both his races this season by a narrow margin, chasing home Crossed Baton at Epsom and Young Rascal at Chester, while Mildenberger won the Feilden Stakes at Newmarket, but was put in his place by Roaring Lion at York last week.
Speaking of Mildenberger, Johnston said: “The owner also has Dee Ex Bee, who is in the Derby. He ran really well at Chester and I think if one of the two runs, it is more likely to be him.”
Another Classic contender for the yard is Elarqam, who was fourth in the 2000 Guineas and he will head to the Curragh on Saturday.
“Elarqam should go to the Irish Guineas and all is great, couldn’t be better,” said the Middleham handler.
David Menuisier, meanwhile, is in no rush to firm up plans for Thundering Blue after his impressive win at York last week.
The grey bolted up from a handicap mark of 93 and Royal Ascot is now on his agenda, as long as the ground is not too fast.
Menuisier also has his eyes fixed on a return to York for the John Smith’s Cup in July.
“There’s a little bit of time to think about which race at Ascot. He’s come out of his race fine and I’ll decide in the next few weeks,” said Menuisier.
“There are a few options, obviously, but it will also depend on the ground.
“If it was rattling fast I wouldn’t be keen on running him so it’s all up in the air.
“We think he’ll stay a mile and half so we do have more options now.
“He looked impressive at York. We may look to stepping him up in class, but we also have to consider the John Smith’s Cup back at York in July.
Mick Channon, meanwhile, would not be scared of plunging Certain Lad in at the deep end at Royal Ascot after his impressive debut win at Redcar.
Heavily backed – he was available at 7-1 early before being sent off the 11-4 second favourite – Certain Lad showed his rivals a clean pair of heels in the six-furlong Racing UK-sponsored Novice Stakes.
“We thought he was okay and he’d been working well with most of the two-year-olds,” said Channon.
“It’s the colts, in particular, that are very good this year. I’ve never had a batch like this, I usually have good fillies.