Promoter Eddie Hearn has revealed the pair are keeping tabs on each other but says any talk of a fight happening soon is premature.
Fury, 29, has been out of action for over two years and still has licensing issues to deal with as the former world champion bids to prove his fitness and mental state to the British Boxing Board of Control.
“I spoke to Tyson Fury this morning,” Hearn told Sky Sports News. “He even got in contact with Anthony Joshua at the weekend, so we’re all talking.
“Let me tell you, that’s a fight that we would sit down now and make for 2018.
“I’ve already seen that he wants 60-40, Tyson Fury, which is not quite the idea that we have, but we are up for making the Tyson Fury fight.
“It won’t be next, because we know what we’re trying to do next. We’re trying to clean up the division and win all the belts, but if it has to be the one after in the summer or have to be after that.
“We are prepared to sit down and make that fight now with Tyson Fury and Anthony Joshua is as well, because he called me straight after Tyson was texting him the other day.”
On Fury’s own situation, which it is claimed will be handled by rival promoter Frank Warren, Hearn added: “Realistically, Tyson talks about getting in the ring in April, fighting Joshua. That’s not going to happen.
“We can’t base our career on a guy that still has what six or seven stone to lose and doesn’t have a British Boxing Board of Control licence, that hasn’t boxed for two years.
“We’re desperate to see him back. We’ll even give him a fight. It will be a massive return, but we are prepared to make the Tyson Fury fight for the summer or for the winter of 2018, unquestionably, but let’s see him back.
“You do not want to go in the ring with Anthony Joshua, having been out of the sport for two-and-a-half years, especially in the physical condition he’s in at the moment.
“Tyson Fury is a great fighter, it’s a tough fight for Anthony Joshua, but it’s one we want, it’s the one the British public want, and we will make that fight,” said Hearn.