Susan Aitken spoke out after a “historic” result saw the SNP become the largest party in the authority for the first time in its history.
Labour has been in power in Glasgow since 1980, but as its vote slumped in the Scottish council elections, the party lost the majority it had in Glasgow.
There are now 39 SNP councillors in the city, compared to 31 from Labour. The Tories - who previously had just one councillor - now have eight, while the Greens also made gains, winning seven seats.
SNP leader and First Minister Nicola Sturgeon has said it is for Ms Aitken, the leader of the SNP group in the council, to decide whether the party goes into coalition or not.
But Ms Sturgeon said that “certainly a minority administration is far from off the table”.
Ms Aitken said: “We’re very open about talking to our colleagues in the Greens.
“The thing about a PR system is, it is designed to throw up results that lead to co-operation and discussion, that’s what our administration will be all about anyway - we’ve emphasised partnership and co-operation through the city as part of how we will govern.
“So we’re entirely open to doing that. We’ll have conversations with our colleagues in the Greens over the next couple of days, listen to them about what they’d like to do, what contribution they’d like to make.”
She added: “I certainly have no qualms or any fear about governing as a minority administration, and talking to colleagues from other parties on an issue-by-issue basis to get support from them.”
But she also stressed: “Equally, if our colleagues in the Greens, who have done well in this election, if they would like to be able to make a formal contribution we’re up for having that conversation with them.”
Talks will take place with the Greens over the next few days, Ms Aitken said, even though Martin Bartos, the leader of the party in the city, was taken to hospital after a bike accident.
Ms Aitken said: “Very unfortunately poor Martin was knocked off his bike earlier in the week and quite badly injured. He’s OK, he is bandaged up in hospital with a broken collarbone and broken ribs and all sorts of things.
“So we don’t want to put Martin under any more stress than he is already, but equally I’m sure he wants to get going on these things as well, and I’m sure we can find ways to communicate.”
She added: “Modern technology can do wonders and Martin has been my colleague for the past five years, we have conversations all the time, this is another conversation, but perhaps on a slightly higher level than the ones we’ve had before.”
Ms Aitken hailed the SNP becoming the largest party as an “historic moment for the city”.
She said: “The city chambers in Glasgow has been run by Labour for decades now, mismanaged some might say, and clearly the people of Glasgow thought it was time for a change, time for a fresh start, and they’ve put their faith in the SNP to deliver that fresh start.”
SNP councillors are “ready to start and hit the ground running”, she added, saying actions would include “getting much better bins in the streets to make our city much cleaner” and repairing potholes in the roads and “getting the pavements fixed to make a much safer city” for walking.
Ms Aitken also said the SNP would be looking to replace old lampposts with LED ones to create a “greener city”, and would seek to improve wifi connections across Glasgow.
“There’s a whole number of things that we want to get started on, that we believe we can make quick progress on, so that the people of Glasgow will see a difference,” she said.
“This was never about getting power for the sake of it, or getting rid of Labour for the sake of it, it was because we believe we can create a better city, we can make improvements for Glasgow’s neighbourhoods and Glasgow’s citizens.
“That’s why we’re in there and that’s what we want to get started on.”