Political groups have been considering potential alliances with each other after the council was once again left with no party having overall control following the election.
The results of Thursday’s poll left the Conservative group with 16 seats, the Liberal Democrats with 15, Labour with seven, and the Progressive Portsmouth People (PPP) with two. There are also two independent councillors. A majority requires 22 seats.
Both the Tories and Lib Dems have told The News they each have a mandate to run the council.
But they will need to secure support from the smaller groupings in the likely event a leadership vote takes place at the council's annual general meeting next Tuesday.
Now the Portsmouth Labour group has confirmed it will be negotiating with the Lib Dems this week – potentially opening a path to a Lib Dem administration.
Group leader George Fielding has said his party is in a ‘strong position’ but will also be speaking with other parties.
Cllr Fielding said: ‘During the election campaign we were quite clear we would not put the Tories into power.
‘However, it really depends on negotiations with the Lib Dems as to what the future of the leadership will be like.
‘We are in a very strong position to influence the administration with our manifesto. We have brought forward our group meeting to this evening and we will be talking with other parties between now and Thursday.
‘We have to make sure we are doing what is right for the city. I think it's going to be a very tight vote on Tuesday.’
Cllr Linda Symes,an independent, has said she will be using her leadership vote to support her former Tory colleagues.
The Eastney and Craneswater representative was suspended from the group last year after alleged racist social media posts.
A Tory internal vote as to whether to have her back in the party is set to take place in June.
She said: ‘I hope to be rejoining the group soon. My vote will be aligned with theirs. It's all to play for.’
The PPP group previously said it would be willing to work with the Lib Dems.