Laxey Partners said they would support Mr Stockbridge's re-election at the AGM on December 19 - but only if he repaid the bonus.
The Isle of Man-based firm became the largest shareholders in the club last month when they bought another £1.3million stake.
Laxey now owns 11.64% of Rangers International Football Club plc.
Mr Stockbridge has repeatedly been criticised by supporters for accepting a £200,000 bonus, when Rangers won last season's Third Division title.
The shareholders seeking change in the Rangers boardroom, including businessman Jim McColl, previously said Mr Stockbridge's position was "completely untenable".
The Rangers Union of Fans, said they had impressed upon Colin Kingsnorth of Laxey the need for the appointment of "trusted directors".
They 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 £200,000 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."
The club said Mr Stockbridge had agreed to return the bonus.
A board spokesman said: "The fans group went to Laxey seeking to get Laxey to withdraw their support in entirety for the board and to support the requisitioners.
"Mr Kingsnorth refused. But he did concede that he would only support Brian Stockbridge if the bonus was paid back.
"The bonus issues only related to support for Mr Stockbridge.
"There was not any question that Mr Kingsnorth wouldn't support the other board members."
Mr Kingsnorth indicated Laxey would continue to back the board and fans said they remain "unclear on the reasoning behind this".
Rangers Union of Fans urged all supporters to vote at the AGM.