In a statement to the BBC, he said "the voice of opposition in the Mournes is greater than the voice of support".
He said he was continuing to take stock on the full range of views but "a national park cannot be imposed and as things are - there won't be one in the Mournes".
Northern Ireland is the only part of the UK without a national park.
A national park is an area of protected countryside administered by its own independent government-funded body to look after its conservation and promote its benefits.
The minister has previously indicated he wants two to be created, with the  Mournes, the Causeway coast, the Antrim Glens and Fermanagh Lakelands  identified as possible areas.
There are 15 national parks in Great Britain and six in the Republic of Ireland.
More than 1,000 people attended a public meeting in September in Newcastle, County Down, where farmers and local residents voiced their opposition to the Mournes being designated a national park.
Environment Minister Alex Attwood has said he will not impose a National Park in County Down's Mourne Mountains.