Earlier this year, Bridges said his caucus had publicly ruled out a post-election deal with the party.
"I don't believe we can work with NZ First and have a constructive trusting relationship," Bridges said at the time.
But in his first press conference as leader, Muller left the door open for reversing this call.
Speaking to RNZ this morning, Jones appeared to be optimistic about the prospect of working with National under Muller's leadership.
"I don't know if he's a beach boy but I do sense coming from [him], good vibrations in contrast to Paula and Simon".
Asked to elaborate, Jones said he meant that the "vibrations are a lot better" – in other words, there appears to be less animosity.
He said there was a lot of "animus" from National towards his party under Bridges.
"Simon Bridges, unfortunately, had personalised his dislike of the New Zealand First party and I suspect that the current leader is going to take his time and work in a more effective fashion realising that rule 101 in politics is you have to learn to count," Jones said this morning.
Jones is highly likely to run in the Northland electorate.
Prime Minister Jacinda Ardern has already ruled out not standing a Labour candidate in the electorate to give Jones a better shot at winning.
Asked about this, Jones said: "The latest signs from the Prime Minister [are that] it's a cold shoulder to New Zealand First in Northland".
But he said that was "Labour's call".
"What National do in Northland – it's all part of the exciting algebra that's going to grow as we count down the 120 days."