The two parties held talks today, with Green councillors Rob White and Melanie Eastwood looking for a number of concessions in return for their support, including a legal challenge against Wokingham Borough Council over changes to the Maiden Erlegh School catchment area.
The Greens also want problems with parking in Newtown addressed, a borough-wide home insulation scheme and the rolling back of some of the cuts made by the previous Tory-Lib Dem administration, including the already approved overhaul of adult social care.
Cllr White said his party is not asking for any cabinet positions and refused to say what Labour want in return, but added: "The talks have been productive, talking to them about what we would want in return for support of a minority administration. We think it would be good to remain independent and take things on an issue by issue basis."
The negotiations are likely to continue into the middle of next week, with more inter-party discussions and individual group meetings scheduled for Monday and Tuesday.
The power vacuum follows last week's local election when Labour increased its seats to 22, the same as the ruling Tory-Lib Dem Coalition - although Lib Dem Warren Swaine remains suspended from his party - with the Greens adding their second councillor to the chamber.