The city is a prime target for the SNP in May's local elections and Mr Salmond said the party would be working "very hard" to wrest power from Labour.
His deputy and Glasgow Southside MSP, Nicola Sturgeon, also claimed voters were seeking change.
She said: "I've lived in Glasgow for 20-plus years and I've never known the mood that there is in Glasgow just now, which is a mood of wanting change and disillusionment and disaffection with Labour.
"So I think we have a great chance and a great opportunity but we don't take anything for granted.
"We won the victories [of] last year because we worked really hard for every vote and that's what we will do again.
"At the end of the day, the result is down to the voters but we'll be working hard because I think the city does really need new leadership."
Mr Salmond and Ms Sturgeon were speaking in Glasgow where the SNP's spring conference takes place this weekend at the SECC. The First Minister said the conference would be a launch pad for elections in which the party is fielding 600 candidates – about 150 more than at the last election in 2007.
The SNP's success at last year's Holyrood elections also followed a party conference in Glasgow. Around 2000 delegates, exhibitors and observers are expected at the conference, making it the biggest spring conference the party has held.
The party says membership has risen by 2400 since the New Year and its business convener, Derek Mackay, added: "Last year in Glasgow we were preparing for what became a historic result in May with the election of the first-ever majority SNP government.
"We won last year's elections, we are working hard to win this year's local government elections for the people of Scotland and we are working to win the referendum for Scotland's future."
Meanwhile, the Scottish Government has sent a list of 36 infrastructure projects to the UK Government, which it says could go ahead now if funding were made available.
The projects, totalling more than £300 million, include motorway improvements, university facilities, schools, housing and investment in enterprise facilities.
The Scottish Government said the "shovel-ready" projects were close to, or had already completed, the planning and procurement process and were ready to get under way.
It wants Westminster to allow Scotland to bring forward capital funding from future years, so work can get under way now.
Infrastructure Secretary Alex Neil said: "The Scottish Government has always been clear that investing in our infrastructure is one of the primary ways to create jobs and stimulate growth."
He added that Prime Minister David Cameron, when he met the First Minister in Edinburgh last month, had accepted the principle of bringing forward capital investment but there were no suitable "shovel-ready" projects in England which could receive funding to begin in 2012 or 2013.
Mr Neil said: "That is not the case in Scotland, and the First Minister made that clear, and suggested supplying a list highlighting where opportunities exist.
"We have done that, showing there are valuable projects that will boost the economy and provide work right across Scotland that are ripe for investment now."