Jones on Sunday again denied having a Zoom interview with Japanese officials just days before coaching Australia at the World Cup in France, saying the Sydney Morning Herald report was "a red herring".
McLennan, who was ousted on Sunday night, says he is meeting with Jones on Tuesday and hopes to get to the bottom of the months-long saga.
While he is giving Jones the benefit of doubt, McLennan says if the reports are true, "that's terrible and appalling" and "absolutely" poor form from the former Wallabies coach.
"Especially when you're leading into a World Cup and your focus should be on the team," he said.
"(But) I haven't seen the proof. I want the absolute proof.
"I'm actually seeing him tomorrow. I've been promised that I'll see the proof at some point and it'll come out and I just want it to be 100 per cent confirmed that it happened in the fashion in which it was reported.
"So, yes, if he did do it, terrible form, especially when you're coaching a national team.
"But let's wait and see the evidence."
RA chief executive Phil Waugh initially took Jones on his word and, after Jones quit three weeks ago, said it was time to move on when asked why the governing body didn't question the coach further.
McLennan also defended RA's decision not to grill Jones, who has since expressed interest in coaching Japan again - having steered the Brave Blossoms to a famous win over South Africa at the 2015 World Cup.
"He made several statements and denied it completely," McLennan said.
"We were leading into other games within the World Cup and he had denied it publicly on several occasions.
"So to go in and try and unsettle the coach further and ask a question where you know what the answer is going to be (would not be wise).
"Phil Waugh had spoken to him and others and he denied it and his agent said that it was completely untrue."
Jones on Sunday told James Graham's "The Bye Round" podcast that it would be madness to have been talking to Japanese officials about coaching their national team while already on a five-year contract with the Wallabies.
"It's a red herring, an absolute red herring," Jones said.
"Conversations go on all the time. People, agents ring you up (but) I didn't have any ... Why would I have signed for five years and taken a young squad (to the World Cup)?
"If I was going to go to somewhere else, why would I take a young squad and put myself out there?
"I could have just taken the solid players and fans love senior players.Â
"So if I was intending to go somewhere else, why would I take a young squad unless I'm a lunatic?
"I'm probably close to but not a fully lunatic."
