A club spokesman confirmed the finance director was in the process of paying back money to the club after it emerged that major shareholder Laxey Partners had demanded the gesture in return for its support at next week's annual general meeting.
Of the five Rangers directors bidding for re-election on December 19, Stockbridge has come under the most pressure after it emerged he had doubled his salary by claiming the bonus for the club's Third Division title win, despite presiding over operating losses of £14.4million.
Rangers fans reported failure in their quest to persuade Laxey founder member Colin Kingsnorth to use its 11 per cent stake to reject the current board and back the four men bidding for election - former Ibrox chairman Malcolm Murray, Paul Murray, Scott Murdoch and Alex Wilson.
Representatives of the Rangers Union of Fans, which encompasses most of the organised supporters' groups, said they had held meetings with a number of significant shareholders in London over two days.
A statement from the group added: "Mr Kingsnorth is now fully briefed on the fans' feelings and appeared to share the majority of our concerns on Mr Stockbridge.
"He also revealed that he had insisted that Mr Stockbridge repay his £200k bonus from last year or that Laxey may not support his re-election.
"He believes that in response to this possible loss of significant shareholder support, Mr Stockbridge had returned, or would return, this money prior to the AGM. He also acknowledged that this was far from the only issue with Mr Stockbridge."
The statement added: "Despite broad agreement on fans' concerns, Mr Kingsnorth indicated that Laxey were unlikely to change their already submitted and publicly stated vote. "We remain unclear on the reasoning behind this, particularly given these shared concerns."
Kingsnorth was unavailable for comment when Press Association Sport contacted Laxey Partners with the claims.
The union urged fans to make full use of their 12 per cent stake after the current board strengthened its grip on power as Sandy Easdale increased his voting influence.
A statement to the stock exchange revealed that Easdale, who sits on the football club board and is the brother of PLC board member James Easdale, had been assigned the voting rights of Beaufort Securities, which has a stake of about three per cent.
Sandy Easdale now has voting rights over 26.6 per cent of Rangers, a block which includes his own 4.5 per cent stake.
Meanwhile, Rangers manager Ally McCoist insists he has been put under no pressure to sell players in January.
McCoist was responding to speculation surrounding the future of left-back Lee Wallace, who has been the club's top performer over the past 18 months and recently won a Scotland recall.
McCoist told RangersTV: "I've had discussions with board members and the chief executive and there has certainly been no indication at all that we have to sell.
"If that's the case, I'm sure I'll be informed of that but until that moment comes we obviously want to keep hold of our better and best players.
"You'd have to say Lee certainly comes into that category and in moving forward, which the club hopes to do, we'd be delighted to keep our better and best players.
"The fans deserve the best team we can afford to put on the park and which can play the best football and entertain 36,000 season ticket holders.
"Home crowds of 45,000 would tell me the fans deserve a good product on that park and we're trying to give them the best side we can."