The England coach was critical of the Australian media's behaviour during his side's tour in June, and highlighted concerns over the Wallabies scrum ahead of this weekend's clash.
Cheika has been riled by his compatriot's behaviour and lashed out at England's pack, while also warning Jones risks ruining his "legacy" with further outbursts against his home country.
Jones is not concerned, though, and insists he is solely focused on making England into the top side in world rugby.
"Obviously Michael Cheika's had a lot to say this week, I'm disappointed he's upset but in terms of where we are we've just been focusing on our game," Jones said.
"He's made some comments about legacy, well we don't have anything to do with legacy, it's an uncontrollable part of what happens so we're not perturbed about that.
"We believe that when we went on the Australian tour staff and players behaved in a very respectful manner. I reinforce again that I feel the Australian media was disrespectful when we were down there, so I don't hide away from those comments.
"He [Cheika] is obviously upset, I'm disappointed he's upset, we'll have a cold beer in the dressing room after the game and he's quite welcome to join us. I don't control his emotions."
Jones confirmed he will meet with referee Jaco Peyper ahead of Sunday's Test, and extended the invitation to his opposite number despite their strained relationship.
"We've got a meeting on Friday at 3:30, we've got all the green tea set out, ready to go," he said.
"We've extended the invitation [to Cheika] it'll be up to him whether he accepts it or not. I'm not too worried about who is going to attend."
On the game itself, Jones described the Wallabies clash as the "most important" of his reign and he expects another big effort from his players to finish the year unbeaten.
"Big game this week, we've really worked hard but smart, we're playing against a very good team, we know they’ve improved a lot since June," he continued.
"Their attack has become more varied, they vary their alignments, they've got some clever two phase plays and we're looking forward to defending against them.
"For us, we've had a good year so far but it's not good enough, we want to finish off with our best performance of the year, so physically we believe we're peaking, mentally we're in a good spot so we've just got to put the wheels into motion on the field.
"We're enormously excited about the game, it's a great opportunity for us to take another step forward."