Local Muslim leader Jalal Chaudry said he would challenge Councillor Shami Khan - who declared his ambition for the Edinburgh East and Musselburgh role on Wednesday - for the Labour nomination to become the first ethnic minority MSP.
Ms Deacon shocked Labour Party members last week with her decision to stand down before next year's Holyrood elections.
Speculation about her likely successor has been brewing ever since, with several city and East Lothian councillors rumoured to be interested.
Portobello councillor Lawrence Marshall today joined Lord Provost Lesley Hinds in saying that he was considering standing while fellow east Edinburgh councillor Ian Perry refused to comment, fuelling speculation that he too was keen on the job.
Former Holyrood minister Iain Gray, the ex-Edinburgh Pentlands MSP, has been tipped as another possible candidate.
Labour Party chiefs are keen to see more people from ethnic minorities and more women standing as candidates for the Scottish Parliament.
It is also widely believed that a person with local experience would be preferred to fill the post - regarded as a safe Labour seat.
Mr Chaudry, 62, a former membership secretary and vice-chairman of the East Edinburgh Labour Party, said: "I want people to know that there is another ethnic minority person ready to throw his hat into the ring.
"Colleagues in the Labour Party have approached me as having the best chance to replace Susan Deacon. I'm not controversial like other councillors."
Indian-born Mr Chaudry, who graduated from Heriot-Watt University and has worked as a civil engineer with the council since 1972, added: "I'm a professional person, well respected in Scottish society. I have experience of traffic and transportation matters and am on the national executive of the Scottish Labour Party."
Councillor Marshall said: "I'm not going to say no. It has crossed my mind and I've been weighing up the pros and cons. I've a lot of local connections to east Edinburgh. I've lived in Portobello for 27 years and I think a local candidate is preferable."
Elsewhere, Councillor Ewan Aitken, who represents the Restalrig ward, said the post didn't interest him as he is standing for council leadership, while Milton councillor Maureen Child said she was committed to local government.
East Lothian Council Leader and Musselburgh central councillor Norman Murray was among several Musselburgh councillors suggested for the post, while none of the East Lothian councillors were available for comment.
Meanwhile, the Tories have already selected a Leith woman as their candidate for the seat.
Christine Wright, a 54-year-old mature student of journalism and a first-time candidate, says she has already been out canvassing in Musselburgh.
She said: "I work in the NHS running chronic disease clinics so I know what is happening at the front line, so to speak. I believe that people need to be represented by people from ordinary walks of life in order to understand the problems facing them."
The Liberal Democrats said no-one had yet been selected to stand for them in the constituency.
Cllr Shami Khan, Mountcastle
Jalal Chaudry, Ethnic Minority Officer East Lothian Constituency Labour Party
Lord Provost Cllr Lesley Hinds, Muirhouse/Drylaw
Cllr Lawrence Marshall, Portobello
Cllr Ian Perry, Meadowbank
Iain Gray, Former Edinburgh Pentlands MSP and Minister for Enterprise, Transport and Lifelong Learning