The development came as Goals revealed its pre-tax profit for 2012 fell 71.6% to £2.6 million, thanks in part to £1.5m of advisory fees relating to the failed bid and bank charges, although underlying pre-tax earnings were up 3.3% at £9.5m.
Sir Rodney, who has led Goals for a decade, will step down as he approaches his 70th birthday.
Chief executive Keith Rogers insisted his departure from the £43,000 a year role was unrelated to the unravelling of the OTPP deal.
"That is history," he insisted, adding it is the "right time" for Sir Rodney to step back.
"He has got to a milestone age. It seems like the appropriate time now for him to step down."
Mr Rogers added Sir Rodney, a former chairman of Leicester City football club and of the UK Sports Council, will retain an advisory position as honorary president of Goals.
Goals recently recruited as a non-executive director Alex Short, finance director of AG Barr, the maker of Irn-Bru, and a fellow East Kilbride company.
It said it has already interviewed candidates to replace Sir Rodney.
In August, 71.4% of independent shareholders in Goals voted in favour of OTPP's £73.1m approach, shy of the three quarters necessary.
Goals's shares were unchanged at 126p yesterday, trading 12.5% adrift of the 144p price that OTTP, one of Canada's largest pension schemes, offered.
Mr Rogers said the takeover talks had not affected company performance, and denied there was a need to rebuild relations with investors after the rejection of the recommended takeover. "I do not think it has been a distraction," he said. "It tells me shareholders like the company. We look at it as a vote of confidence."
Earnings at Goals were further depressed by a £2m writedown of its £4.7m site in Los Angeles, its first in the United States.
Mr Rogers said this was deliberately bigger than needed as it tested the requirements of the American market. "The US is one of our best-performing centres," he said.
Goals also took a £2.1m hit on development costs for its old-style sites after moving to a modular method and £1.8m on information technology.
Goals, which has 43 sites UK-wide including three in Scotland, saw like-for-like sales rise 1% last year.
Within this football sales, which account for 82% of profits, were up 3% after a 3% price rise in the summer.
But it saw a 4% fall in bar and vending sales as a more fitness- conscious generation of players eschews the post-match pint.
Mr Rogers said Goals is satisfied with its sales performance. "Football has shown itself to be resilient," he said.
The impact of snow had left total sales flat in the first eight weeks of the financial year although they were up 3% on an underlying like-for-like basis.
Goals has halted new site construction as it seeks to pay down debt which fell £3m to £50.2m last year.
Asked if it needed the backing of an investor with large pockets to continue it expansion, Mr Rogers said: "Not necessarily."
He said the pause in building would allow Goals to focus on generating profits from existing sites.
Simon French, analyst at Panmure Gordon, said: "Goals is a solid business with strong management and an option on US expansion but the rehabilitation period has further to run."
Goals announced a final dividend of 1.175p to be paid in May.