The Grime rapper, whose real name is Richard Cowie, was widely condemned for the anti-Jewish posts which he started sharing on Twitter on Friday.
He was banned from the social media site on Wednesday.
Meanwhile, the musician has insisted he is not racist and apologised for “generalising” in his comments.
On Thursday, barrister Jeremy Briar, 39, wrote an open letter to the Cabinet Office outlining why he believes Wiley should have his MBE forfeited.
The rapper was made an MBE for services to music in 2018 but, according to Sky News, he said he would be willing to give it up as he “never wanted it”.
Mr Briar, a barrister and legal commentator, posted his open letter in an eight-tweet thread on Thursday.
He wrote: “Dear Sir or Madam, I have strong reasons to believe that the honour of MBE bestowed upon the musician Richard Kylea Cowie Jr (“Wiley”) should be forfeited by reason of his extraordinary and sustained publication of vicious antisemitic views, during the period 24-26 July 2020.”
Mr Brier later said: “When we give out honours we are effectively bestowing a real legitimacy on that person as a servant of our country and someone that has done very good deeds or contributed in a significant way.
“As a country we can’t be seen to say ‘yes, we give the cloak of respectability to people with extreme racist views’.
“I think we as a country should care about who gets our honours.”
It comes after Wiley apologised in an interview with Sky News.
He said: “I just want to apologise for generalising and going outside of the people who I was talking to within the workspace and workplace I work in.
“My comments should not have been directed to all Jews or Jewish people.
“I want to apologise for generalising, and I want to apologise for comments that were looked at as anti-Semitic.
“I’m not racist, you know. I’m a businessman. My thing should have stayed between me and my manager, I get that.”
When asked if he accepts his comments were anti-Semitic, he told Sky News: “My comments should not have been directed to all Jews or Jewish people.”
Wiley’s manager John Woolf, who is Jewish, said A-List Management had “cut all ties” with the musician following the series of social media posts.
The Campaign Against Antisemitism has said it will contact the Cabinet Office to ask for Wiley’s MBE to be revoked.
According to Sky News, Wiley said he would be willing to give it up as he “never wanted it”.
He told the broadcaster: “I never felt comfortable going to get it. Just look at Britain’s colonialism history.”
