The Upper Bann MLA is the only declared candidate so far to replace Steve Aiken, who announced his intention to resign on Saturday.
During an interview with the BBC on Tuesday morning, Mr Beattie ruled out the possibility of a single unionist party in Northern Ireland and vowed to challenge the DUP.
He said: “We can want the same destination but we can go about it in a different way, and we have gone about in a different way because we have brought about solutions. We haven’t sucked our teeth and stood there with our hands in our pockets.”
“Our job is to challenge them and to stand on our own two feet, and we will challenge the DUP on things we know they have got absolutely wrong.
“We will challenge them at every single level. There will not be one unionist party, that is fact.
“It does not help unionism for the DUP and the UUP to come together.”
The resignation of Steve Aiken, 10 days after DUP leader Arlene Foster was forced to quit following an internal party move against her, has thrown political unionism into further turmoil.
Lagan Valley MLA and former firefighter Robbie Butler is thought also to be considering a bid to be new UUP leader.
Mr Beattie said if he was elected leader he hoped to attract nationalist voters, but ruled out support for an Irish Language Act.
He said: “I absolutely love the Irish language, it’s part of our culture, it’s part of our heritage, it needs to be funded, it needs to be protected, it needs to be cherished.
“I have no issue with the Irish language – my issue is with an Act, because what is being proposed could end up driving more division in Northern Ireland.
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“We can literally have people driving down one street, where signs and services are in English and Irish, and driving down another street where signs are in English and Ulster Scots. To me that is divisive.
“So what I want to do is take the politics out of the Irish language and try and close that gap.”
Mr Beattie also said he would not be taking advice from the Loyalist Communities Council (LCC). Arlene Foster was criticised last month for meeting with the LCC, which represents loyalist paramilitary organisations in Northern Ireland.
He said: “If I meet the Loyalist Communities Council, the first thing I will be asking them is when they will be disbanding and when they will be leaving people alone and getting their foot off the necks of people in Northern Ireland.”
He added: “Let’s not tar all loyalism as paramilitary groups. There is no place in our society today for any paramilitary groups. If they are here they need to go.”
