Abu Rumaysah, who was born as Siddhartha Dhar, reportedly fled the United Kingdom in September while on bail, a day after being arrested in London with radical cleric Anjem Choudary on suspicion of encouraging terrorist activities.
"My 'kind and generous' brother had changed beyond all recognition since converting to Islam and being radicalised, and laid much blame at Choudary's door," said Konika Dhar, sister of the 31-year-old Islamist who is suspected to have joined the Islamic State in Syria.
"I believe that being in prison would be better than where he is now and I want him to realise that as well because his perception of the repercussion is slightly distorted and not accurate and things will be okay if he just speaks to us", Ms Dhar was quoted as saying to ITV news.
Her brother was well-known in the UK for frequent television appearances declaring his wish to live in the "Islamic State".
"I'm sorry if you think Choudary is your role model because he's not," Ms Dhar said in a message to her brother.
Anjem Choudary was arrested in September with eight others, including Rumaysah, as part of an investigation over allegedly supporting the banned extremist group, al-Muhajiroun.