Anas Sarwar insisted the party should instead look to "maximise" its representation.
He also argued "there is a case to be made" for minority administrations.
Council elections are due to take place in May, but the PR system makes it difficult for parties to win overall control of local authorities.
This has previously led to a variety of coalition arrangements, including between Labour and the SNP and Tories.
Elsewhere, Mr Sarwar insisted Scottish Labour election candidates must be pro-UK, as he dismissed reports at the weekend the party could allow candidates to support independence.
He said: "Whoever it was who was speaking or quoted clearly doesn't understand that decisions on selecting candidates in Scotland, even for a general election, are made by the Scottish Labour Party and the Scottish Labour Party alone.
"We will be standing on a platform in the UK general election which is about reforming and renewing the UK, which is, yes, about pushing power out of Westminster and into the nations and regions of the UK, but also pushing it out of Holyrood and into local communities across the country as well.
"And that's what we'd expect every candidate to stand on."
He added: "On the question directly of candidates, we will be a pro-UK party standing for a reformed and renewed UK, and all our candidates would be expected to abide by that manifesto, so that we can have a Prime Minister that is for the whole of the United Kingdom."
Mr Sarwar said he had a "close relationship" with UK leader Sir Keir Starmer, adding: "I've said this to him directly and I say it publicly: when it comes to Scotland, when it comes to Scottish Labour, I'm in charge, I'm the boss.
"We decide Scottish Labour selection processes in Scotland."
In a speech to mark the start of the new year, Mr Sarwar argued Scotland is being let down by the "growing arrogance" of the SNP.
He said: "When politicians or parties begin to believe they are untouchable or unbeatable, they begin to lose touch, become distant and take people for granted.
"I believe that is happening to this SNP Government and that's not good for Scotland."
He said Scottish politics suffers from a "culture where nobody takes responsibility, failings are excused and we have to wait years for action".
Speaking to journalists afterwards, Mr Sarwar was asked if he could rule out Labour councillors entering into any pacts or coalitions with the Tories following the May elections.
He said such matters would be decided by the party's Scottish executive committee.
But he added: “My strong view, and this is a discussion we will have with our colleagues in local government and also with the Scottish executive committee, is I don’t think we should be doing pacts or deals or coalitions."
He continued: “I don’t think we should be looking at coalitions with any political party, but rather looking to maximise Labour representation and winning individual arguments on their merits."
Mr Sarwar later said there were two parties that are damaging Scotland, referencing both the SNP and the Tories in power north and south of the border.
Scottish Tory MSP Sharon Dowey accused Mr Sarwar of "trying to dupe people".
She said: "If Anas Sarwar is against coalitions, why is his party in coalition with the SNP in six councils across Scotland right now?
"He's trying to dupe people into believing something that isn't remotely credible.
"Labour have no chance at forming council groups without going into coalition."
Following the 2017 local government elections, Labour entered into coalition arrangements with the SNP in Edinburgh, Fife, Stirling, East Renfrewshire, South Ayrshire and Dumfries and Galloway.
Nine Labour councillors were suspended by the party after entering into a coalition with the Conservatives in Aberdeen.
Across Scotland, the overall number of Labour councillors fell from 395 to 262.
An SNP spokesperson said: "If Anas Sarwar thinks people across Scotland will have any faith that his Scottish Labour councillors will not enter into coalitions because of their party leader's desires, then he is wildly mistaken.”
Elsewhere, Mr Sarwar said former UK Labour leader Jeremy Corbyn should apologise for the hurt caused by the party’s antisemitism scandal.
He said: "I think that's the least that anyone who has caused pain or hurt should do in that situation."
Mr Corbyn was suspended in October 2020 after he said anti-Semitism in the party was “overstated”.