Chief executive Stewart Regan was unable to corroborate Younis' claims that Yorkshire have offered him the captaincy - but clarified that the Pakistani was one of a clutch of cricketers with whom the county have been speaking.
"Yorkshire are keen to look for a replacement for Darren Lehmann. Younis is one of the people we are talking to," said Regan.
Younis, who on Thursday shocked a news conference in Pakistan by announcing his refusal to captain his country for the Champions Trophy in the absence of Inzamam-ul-Haq, told Bigstarcricket of his Yorkshire offer.
"The great English county team Yorkshire have made me an offer to be their captain for next season," said the 28-year-old Test and one-day international batsman.
Younis added: "Yorkshire have great traditions, and I will be finding out as much about their history as I can before I go there.
"I know players like Michael Vaughan and Matthew Hoggard play there - and also legends such as Geoffrey Boycott and Sir Leonard Hutton played there a few years ago.
"It will be an honour to follow these cricketers and play at Headingley, especially as the captain. The club said they like my energy and the way I have captained in the past, so I hope we can be good for each other."
Yorkshire, meanwhile, are treading more carefully when it comes to public pronouncements - but Regan admitted he was pleased to hear of Younis' remarks.
"We have not finalised any details yet," he said.
"But if he has put it out there, it is quite encouraging from our point of view.
"If it is finalised - and we have a board meeting next week - then we will be in a better position to make an announcement."
Younis is in line to become the third Asian-born overseas player to represent Yorkshire - but if he was appointed captain to boot that would be of particular note for a county with a sizeable home-grown population of sub-continental descent.
The first representatives of that community have begun playing for Yorkshire over the past 12 months - and Younis' arrival would be of obvious advantage in continuing to tap into that mine of talent.
Younis is under no illusions about the challenge of an English domestic season, having already played for Nottinghamshire.
"I enjoyed my spell with Nottinghamshire in 2005 - and although I was only there for about five weeks as Stephen Fleming's replacement, I experienced enough of county cricket to know what it is all about," he said.
"There are many matches to be played, and a full season in England will be tough. But that is what I like about the challenge."
He added he has been in negotiations with Yorkshire for the past month.
"They first contacted me through Ramiz Raja when I was at Cardiff while playing for Pakistan in the first one-day international against England," he said.
"The talks have been ongoing since then, and I am pleased to say that I have agreed their terms and conditions.
"I hope the contract will be completed next week."