Wharton has held shares in the club since 1949, and has been on the board of directors since 1993.
He had a two-year spell as chairman from 2001 to 2003, but returned in 2004 after ousting his replacement Chris Holland.
He has suffered from heart problems and was unable to attend last week's BBC Radio Humberside fans forum or the final two games of the season due to a chest infection.
"I do think it is time to find someone to follow me and that will possibly mean them taking over my investment," he said in an online question and answer session with supporters conducted via Iron-Bru.net.
"However that is not essential as it would not add value to the company's balance sheet. I would rather any investor acquired new shares to gain control.
"I have never sought to control Scunthorpe United. It is a huge responsibility. It was only because other shareholders did not take up their various rights issues, that I effectively acquired a controlling interest.
"I will be actively looking for a successor in the year ahead. I was ready for retirement back in 2003 but it was short lived and I have to say I have enjoyed most of the last seven years.
"There have been numerous very special moments. The reappointment of Brian Laws, and the appointment of Nigel Adkins, with Andy Crosby and Ian Baraclough as his assistants, were all controversial at the time but proved to be very beneficial for our club. This time retirement will mean retirement!"
Rex Garton and Keith Wagstaff appear the most likely candidates from the Iron's four-man board of directors, which also includes Jason Oxenforth.
Wagstaff held the position from 1994 until 2001, when he resigned after criticising the performance of then manager Laws.
Garton is a parter with local law firm Mason, Baggott and Garton who has been on the board for 20 years.
Wharton, reacting to suggestions from some Iron fans to launch a supporters trust to purchase shares, also opened the door for a fans representative joining the board.
"The concept of someone sitting on the board, representing the fans, is a good thing," he said.
"I have absolutely no problem with a supporters trust. I don't however subscribe to the view that a club should be run by a supporters trust. It may appear to be an ideal structure, but the reality is that you have too many differing opinions.
"The fans will always be the heart and soul of any League football club. How you organise them into a trust is always going to be difficult."