Dr John Sentamu, known for his passionate tweeting during the Rio Olympics, urged his followers on Twitter to start a campaign to have the athlete royally recognised.
There have been growing calls for the 33-year-old to be honoured after he retained his 5,000 and 10,000 metres titles at the Rio Olympics, becoming the first British track and field athlete to win four Olympic gold medals.
Farah is already a CBE following his double gold at London 2012.
Mo Farah U are simply the Best Athlete Team GB has ever seen!Absolutely FANTABULOUS&Awesome!Congrats 4 the Double Double!BF Rt:now SIR MO????
— John Sentamu (@JohnSentamu) August 21, 2016
"It'd be amazing, just knowing where I grew up, where I have come from, the journey I have taken," said Farah, who was born in Somalia and came to England aged eight, when asked about the possibility of becoming 'Sir Mo'.
"I didn't even dream of becoming Olympic champion, let alone four times.
"Anything is possible, but for me it is up to the public and the people. I just have to enjoy what I do and keep winning medals for my country because I just love winning.
"But being Sir Mo would be amazing. I remember Sir Alex Ferguson got it because he was at Manchester United, and Sir Steve Redgrave for what he did, and to be able be in the same category as them would be pretty amazing."