Rose opened up alongside players past and present in an upcoming documentary, A Royal Team Talk: Tackling Mental Health.
Per BBC Sport, he said:
"I was speaking to another club in the summer and they said, 'the club would like to meet you, just to check that you're not crazy,' because of what I'd said and what I'd been through.
"I was embarrassed, as whatever I've been through I like to think it doesn't affect me doing my job.
"I still know I'll always give a hundred per cent."
Rose added that the idea some people "assume I might be crazy" makes him "angry" and "embarrassed" and that he would turn down such an opportunity if it presented itself again.
The 28-year-old discussed the issues he faced during a lengthy spell out of the team with injury:
Rose had initially revealed his struggles shortly before the 2018 FIFA World Cup, where he reached the semi-finals with England.
He spoke to The Independent's Miguel Delaney, in which he discussed his uncle's suicide, racist abuse aimed at his mother and a gun being fired at his brother in his home:
Football writer Daniel Storey was among many who praised Rose for talking about the issue so candidly:
The defender also said that playing for England was his "salvation" in difficult times.
The documentary also features Peter Crouch, Thierry Henry and Jermaine Jenas, as well as England boss Gareth Southgate, broadcaster Dan Walker and Prince William.
Three Lions manager Southgate discussed his penalty shootout miss for England in the semi-final of the 1996 European Championships—which saw them lose to Germany—became a career-defining moment and attracted a great deal of media attention.
"For years, people with young kids would introduce me, 'This is Gareth. He was the bloke—do you remember that?' He said. "That's the narrative that goes around your life. I played 700 games but I'm that bloke."
Crouch, 6'7", felt the constant need to prove himself with the Three Lions because he felt "a stigma against" him because of his appearance, which repeatedly brought him to tears during his teenage years.
The documentary will air on BBC One at 10:30 p.m. BST on Sunday.