Mr Paisley said both candidates 'get it' in relation to unionist concerns over the Northern Ireland Protocol, which has created barriers on trade into the region from Great Britain.
He said his "heart probably says" he would support the Foreign Secretary as she has been "more engaged" on unionist concerns over Brexit's Northern Ireland Protocol.
Postal ballots are set to arrive on Tory members' doorsteps by August 5, with a final result due to be announced in September. Mr Paisley said: "Because Liz Truss has been so prominent in pushing the reforms to the Protocol, I think they would think that Liz Truss is probably the person that they could trust the most in taking that forward and delivering it.
"I think my heart probably says I would like to see Liz Truss getting it because she has been much more engaged on this issue. But the DUP has made clear it will continue to block the election of a Speaker, preventing further Assembly business including the nomination of new first and deputy first ministers.
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