The convicted paedophile, 43, is in jail in Kiel, Germany, after being sentenced to 15 months for drug trafficking in Germany and seven years for raping a 72-year-old American woman in Praia da Luz, Portugal – the resort where Madeleine vanished in 2007.
His defense lawyer Friedrich Fülscher told German magazine Der Spiegel the suspect is “in the pillory worldwide” and fellow inmates are trying to bully him over the case.
Mr Fülscher said: “Fellow inmates try to bully him where they can.
“He is pilloried worldwide and easily identifiable.”
The lawyer added: “There has not yet been an official offer of interrogation.
“As a precaution, we have informed the public prosecutor’s office that Christian will only comment on the allegations, if at all, through us.
“He is currently exercising his right to remain silent. However, this does not mean he has something to hide.”
About the suspect, Mr Fülscher said he “makes a calm and friendly impression” and “has never been loud or angry” during their meetings.
Madeleine went missing on May 3, 2007, from the resort in Portugal.
The three-year-old was left asleep in the apartment with her two siblings while her parents were having dinner at a nearby tapas restaurant.
The night before Madeleine disappeared, Brueckner allegedly told him then-girlfriend he had “a horrible job to do”.
His former partner later asked him if he abducted the three-year-old and he warned her “just don’t go there”, it is claimed.
The woman claims Brueckner, then 30, told her: “I have a job to do in Praia da Luz tomorrow.
“It’s a horrible job but it’s something I have to do and it will change my life. You won’t be seeing me for a while.”
A friend of the woman said she did not take Brueckner’s comments seriously that night because she did not think he was capable of doing something terrible.
The friend said: “What he [Brueckner] said at that dinner suggests he planned the whole thing very carefully and that he might even have stolen Madeleine to order.
“But we also can’t help feeling guilty thinking we should have pulled together all the clues years ago and gone to the police.”
A phone call received by Brueckner just before Maddie disappeared placed him in the Praia da Luz area.
It was received on a mobile phone belonging to the suspect at 7.32pm and finished at 8.02pm.
German investigators are now trying to trace the owner of the phone used to call Brueckner on the night Madeleine disappered.
Hans Christian Wolters, the German prosecutor heading the investigation, suspects that a member of the Ocean Club in Praia da Luz may have helped the prime suspect target the apartment where Madeleine was asleep.
Mr Wolters said: “This is of interest to us. The phone call made by the suspect could be between him and a member of staff who told him when to break into the McCanns’ apartment.”
German police said they want to trace the person who called Brueckner before they interview the suspect in prison, The Sunday Times reported.
They added there is no evidence the employee knew about Madeleine’s kidnap in advance, but speaking to the person who made the phone call could help them understand what happened that night.
Mr Wolters said: “At the moment if we interview the suspect he could say, ‘My girlfriend had my phone that night and I didn’t have it’.
“The person he spoke to could put the phone in his hand [by confirming that it was definitely Brückner to whom he spoke], which would mean he was in the area at the time.
“This is the evidence we want before we issue an arrest warrant and then interview him for the murder. It would help the case against him — but we would also need more evidence.”
German authorities said they were working on the assumption that McCann is dead, though authorities in the United Kingdom continued to treat her disappearance as a missing persons case.
It comes as it emerged Brueckner could be released from prison on July 17 if the European Court of Justice overturns his conviction for raping a woman.
He is challenging the conviction because German police extradited him from Portugal for a separate drugs conviction, but then put him on trial for rape.
His lawyers are arguing that this was illegal.