The Scottish Labour leader said those standing in the race need to allow colleagues at Holyrood to determine the party's stance on issues such as the constitution.
Last year, shadow chancellor John McDonnell was criticised by some within the party after he intervened in the debate by saying Labour would not block another referendum from being held.
Speaking on a visit to a Men's Shed in Shettleston on Friday, Mr Leonard said: "I've made clear to all of the candidates that in my view decisions on the Scottish constitutional question, for example, should be made by the Scottish Labour Party.
"I've also made clear that the next big electoral challenge the Labour Party faces in the UK are the Welsh Assembly and the Scottish Parliament elections in 2021.
• READ MORE: Richard Leonard: Why Scotland now needs an urgent devolution plan"So we will be looking for support, we will be looking for political and organisational support in this elections."
He added: "We are a party which is organised right across these shared islands and I think that's a strength.
"From what I've tried to say to anybody who's standing, either for the leadership or the deputy leadership of the Labour Party, is that it's good that they are understanding that Scotland is a key battleground for the Labour Party if it is to win power back at a UK level, but they need to listen to the Scottish Labour Party."
• READ MORE: SNP’s independence plans would leave £100 billion bill, says Richard LeonardMr Leonard also reiterated his position in favour of home rule within the UK, although outlined his view that having such an option on the ballot paper in any future independence vote would prove difficult.
"Home rule is a long-standing tradition of the Labour Party," he said.
"We have always envisaged a strong Scottish Parliament but within the United Kingdom so that we would still send MPs to Westminster, that we would still see that the pooling and sharing at a UK level of defence, foreign policy, elements of macroeconomic policy, pooling and sharing of welfare, makes a huge amount of sense.
"If we're going to see a redistribution of wealth and power, which as a Labour Party is something we stand for, then it makes sense to do that at a level where there can be a meaningful redistribution of wealth from the very rich to the poorer parts of society.
"I think that makes sense to be implemented at a UK level."
He added: "There are things that we can do in Scotland as well but I think a lot of that makes sense to he done at a UK level.
"We're clear that we do not favour a second independence referendum. We are not in favour of independence.
"The offer has been made in the past by Nicola Sturgeon to other parties to consider whether a third question could be put on the ballot paper.
"There are, I have to say, some difficulties in understanding how exactly that would work. So it's not something that we're actively promoting."