Haye, a former two-weight champion, admits his own training preparations have been disrupted in the past, but urged Joshua to press ahead with his stringent training regime, regardless of the opponent.
“It’s very difficult. I’ve had it in my career when you’ve had a last-minute switch,” Haye said.
“All your sparring partners are geared up to be like Miller. For all he knows, he fights someone five inches taller, and a southpaw, you don’t know what he’s going to do.
“What he needs to focus on is just focus on himself, to be the best Anthony Joshua possible, train hard, stay focused. He’s going to have someone in the ring with him on June 1, hopefully we can just get someone in the ring who isn’t going to be on the big stage for the first time.
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“He needs an opponent who has been out there and has performed on the highest level, and there are a few names out there. There’s not many, but there’s a few names out there that would get people excited.”
In his new role as Derek Chisora’s manager, Haye is guiding the heavyweight’s career ahead of this Saturday’s must-win fight against Senad Gashi at The O2, live on Sky Sports.
And he even contacted promoter Eddie Hearn to suggest that Chisora would be willing to step in as a replacement for Miller.
Haye said: “I believe Anthony Joshua needs an opponent who doesn’t get fazed, an opponent who has got a history of challenging for world titles, and producing the goods on the night.
“For me, obviously I got a call from Derek Chisora this morning, who has a fight this Saturday, and he said ‘Listen, chuck my name into the hat, I’d love that opportunity. I’m a prizefighter, I’m 35 years-old, I’ve shown against Dillian Whyte that I have what it takes at the highest level’.
“He was winning that fight against Dillian Whyte who was ranked at No 1 by many of the governing bodies. He believes now, with a new coach, Dave Coldwell, he can go that next step, and not only challenge for a world title, but win it.”