Graves sensationally quit from the board of Nisa-Today's in a speech at the Costcutter annual conference last week, claiming he had been barred from meetings because of a conflict of interest.
However, Graves, who has been on the board for 20 years, has now written to the buying group to explain that his resignation was not necessarily permanent and that he reserved the right to re-join the board at 30 days' notice.
As part of Costcutter's contract with Nisa-Today's, the retailer has a place on the board. "Costcutter still has the right to appoint a director, although there are no current plans to do this," a spokeswoman said.
Graves' request comes as Costcutter increased sales to £609.5m in the year to 25 April. Pre-tax profits rose 10.8% to £10.6m during the period, according to accounts filed at Companies House.
Costcutter had outperformed the market as shoppers chose to shop little and often, said CEO Nick Ivel. However, store numbers dipped slightly from 1,541 last year to 1,536.
"Our results reflect the support we have given retailers over the past year," he said. "We have worked closely with them through the recession, taking measures such as providing free themed PoS leaflets for retailers to generate maximum impact in-store and to increase basket spend."
Costcutter was in the middle of an extensive marketing programme, and had recently increased TV exposure with ads featuring former cricketer Darren Gough, Ivel said.
It also added 89 new retailers in the first quarter of the year and achieved its first-ever £13m sales week during the World Cup. "Helping our retailers to future-proof their businesses through store development has helped ensure retailers are trading to the best of their potential," Ivel added.