But some senior figures within the local party have expressed concerns that the person to succeed Mr Denham should have roots in the city.
A freelance journalist who has contributed to a number of national newspapers, she is a current member of Southwark Council having been elected in 2011.
She has visited Southampton regularly for the past year before moving to the city permanently, and says that in that time she has built up a wide knowledge of the city and its history.
She said: “I just think there are so many good things here we can achieve. This is a fantastic place to live with fantastic people living here, and I want to tell everyone about that nationally.”
The 28-year-old said she would fight to bring more skilled jobs to the city, make Southampton a living wage city and tackle deprivation and unemployment.
Ms Davis says she has “already won the backing of the head of the port”, Associated British Ports director Doug Morrison, who is quoted on her website as saying: “I believe she has a huge amount to contribute to our community.”
Mr Morrison was unavailable for comment last night.
The website also has a comment from Bitterne Park Secondary School head teacher Susan Trigger, saying: "She is clearly very passionate about education".
However Mrs Trigger said last night denied that she had endorsed Ms Davis or any other candidate, saying: “All I did was confirm that she had in effect done her homework in my view in understanding the schools in the area.
“We haven’t endorsed anybody.”
Ms Davis added that there may have been some “ambiguity” over the inclusion of Mrs Trigger’s comments as an endorsement, and that the section had been changed to “what people are saying”.
A senior figure in the local Labour hierarchy, who wanted to remain anonymous, told the Daily Echo: “Going back to the 1970s the candidate has always been a local person as they know about local issues and that background is beneficial.
“My personal view is that I have always wanted a local candidate.”
Two other candidates on the all-women shortlist were revealed by the Daily Echo earlier this week. City councillors Sarah Bogle, 44, and Satvir Kaur, 28, are also in the running to succeed Mr Denham who will stand down at the next general election, expected to be in 2015.