A new YouGov poll for the Evening Standard puts Dame Tessa ahead of all other known rivals with 17% of poll respondents naming her as the best potential candidate.
Only comedian Eddie Izzard beat the Dulwich and West Norwood MP, securing the backing of 21% of respondents.
However Izzard has repeatedly said he won’t consider standing before 2020.
Labour MP Diane Abbott, recently sacked from the party’s front bench, and former Transport Secretary Lord Andrew Adonis attracted the support of 9% and 6% respectively.
David Lammy and Sadiq Khan, both regularly claimed to be the front-runners for the nomination, scored the backing of just 7% and 5% of respondents.
Ms Jowell enjoys the highest cross-party support of any likely runner with 29% of Liberal Democrats and 17% of Conservative voters backing her.
She also has a clear lead among Labour supporters with 20% naming her the best candidate, 7% more than selecting the second-placed Diane Abbott.
Labour says it will select its candidate through a primary in which both party members and non-members will be able to vote.
