Fury made the claim in a video on social media having called out his rival, saying he has left Joshua with "no excuses" not to take the bout.
Joshua's promoter Eddie Hearn expressed scepticism about Fury's initial offer, also made on social media on Monday, but said he was willing to discuss it with his counterpart Frank Warren.
Fury said: "I'm being bombarded with messages on how much I'm going to pay AJ - everyone is saying 80-20, 70-30, 75-25.
"The actual answer is I've offered him 60-40 - 40 per cent of this amazing fight because I want this fight to happen.
"He doesn't have any excuses now not to take it. He can't say I've low-balled him and offered him 20 or 30 per cent. I've offered (his) people 40 per cent - take it or leave it."
Joshua suffered a second straight defeat to Oleksandr Usyk in Saudi Arabia last month but Fury's hopes of landing a bout with the Ukrainian were dashed when Usyk said he did not intend to fight again this year.
Hearn had previously said they were considering options for a return for Joshua early next year, but suggested if the offer from Fury's camp stood up, then it could happen.
"Fury's outstanding at getting the public to believe absolute nonsense," Hearn said on talkSPORT. "It worries me actually what people do believe, if you look at the timeline over the last two or three weeks, it's unbelievably bizarre.
"Personally, I don't believe Fury is serious about this, but if he is, which I said to the Warrens last night, 100 per cent we will sit down and make the fight.
"I would love to get really excited about this, because it's the fight that I get stopped in the street for more than any fight that could be made and it's a fight that AJ has wanted for a long time.
"Don't forget, we signed for this fight last year before the arbitration forced the Deontay Wilder fight for Tyson Fury.
"The message is quite clear from AJ, we don't want to get involved in a backwards and forwards, we want the fight, it's the fight he's wanted for a long time.
"We had plans after the Usyk defeat to come back in December and then go again in March, get active and get the rhythm going again and then try and fight for the world heavyweight title.
"But, I know having spoken to AJ, if that fight is there and they're serious, which I have my doubts about, but for the good of trying to make it happen let's believe Tyson Fury.
"I said to George Warren from Queensberry last night, get the details and the offer over to us and I'll take it to AJ, he's ready to go.
"We didn't expect this opportunity, but it's a great opportunity to fight for the world title in the biggest fight in boxing and we will definitely look at it."
Fury's promoter Frank Warren said they were set to send a "written offer" across to Hearn on Tuesday, with the proposed bout to take place "in the UK and hopefully in November."
Warren added on talkSPORT: "It's us who have made the approach to give AJ a great opportunity to get himself back into the top level against the world champion Tyson.
"He's willing to make that voluntary defence, so we'll send the offer across today and then they'll have to look at it and decide whether they wanna grab this with both hands.
"To his credit he has come out saying that he's up for it. I'm not bad-mouthing them or the other side, all we're interested in doing is making this fight."