Jess Phillips, who bookmakers currently rank as an outsider in the leadership race, said she was opposed to an IndyRef2 and instead wanted to discuss issues "relevant to the lives of people in Scotland".
But the SNP said the MP for Birmingham Yardley’s comments “smack of arrogance and the same high-handed, dismissive attitude that caused support for Labour to collapse in Scotland”.
Ms Phillips was speaking on BBC Good Morning Scotland, just hours after her party colleague and leadership rival Rebecca Long-Bailey criticised Labour's involvement in the successful 2014 Better Together campaign which argued for a No vote at that year's referendum.
The party has entered a steep decline in Scotland since then, losing all but one of its MPs north of the Border at the 2015 general election - a result it managed to repeat at last month's UK poll.
Labour also struggled to portray a unified stance on the IndyRef2 issue during the 2019 election campaign, with Mr Corbyn facing repeated attacks from the Conservatives over his perceived weakness on the issue.
Nicola Sturgeon is demanding the right to hold a second referendum after the SNP won 47 of 56 Scottish seats last month.
Speaking today, Ms Phillips said that not having a clear position on Scottish independence and Brexit was a key reason why the party has lost elections.
"I think that some of the reasons that we lost in Scotland and have been losing in Scotland for some time - this isn't wholly down to the last general election - is that we have, since the referendum up there, not necessarily had a clear position on the two big constitutional questions of the day," she said.
"I think that people, when they look at a political party, if they are not certain on what they are saying on any one thing, they lose trust with the public."
She added: "I don't think we should have another referendum on Scottish independence - 53% of the Scottish public in the general election did not vote for a party that was promoting independence.
"I think that we should be talking about things that are relevant to the lives of people in Scotland. I can't see a circumstance where I think it would be better for Scotland to leave the UK."
Scottish Conservative chief whip Maurice Golden said: “Labour leaders on both sides of the border have been repeatedly weak on independence and the question of another referendum.
“Voters in Scotland have been betrayed by lip service paid to the union, and will have no cause to think Jess Phillips is any different.”
Tommy Sheppard MP said: “These comments smack of arrogance and the same high-handed, dismissive attitude that has caused support for Labour to collapse in Scotland.
“Labour clearly hasn’t learned a thing and is still hopelessly out of touch if it thinks it can ignore democracy and deny people in Scotland a choice over our future.
“As long as Labour politicians think they can lecture from Westminster and refuse to respect Scotland’s right to self-determination - they will continue to fade into political irrelevance.
“The SNP won a landslide victory at the General Election, with over 80 per cent of Scotland’s seats represented by the SNP on a mandate of protecting Scotland’s right to choose its own future - and the people of Scotland will have that choice.”