"We are expanding and are looking at everything at present, including FQR's stores," he told The Grocer.
The executive chairman made the comments this week as the group reported sales to retailers up 10.3% to £324m in the six months to the end of September.
While some of the sales growth was caused by inflation, underlying sales were up 6%, he claimed.
Store numbers had grown by 45 over the six-month period to about 1,600 and there was still potential to open many more stores across the UK, he said, adding that a further 200 stores were to be refurbished.
"We have new stores opening all the time and we're seeing significant volume growth too," he said. "This growth is partly being fuelled by the various loyalty schemes available to our retailers such as New Era Trading Terms. At Costcutter we deliver the complete package of support to our retailers."
Costcutter's sales would continue to grow as consumer confidence returned and the economy recovered, predicted Graves.
A new TV campaign featuring Darren Gough would also help attract more consumers, he said.
One third of First Quench stores were not profitable, says KPMG (7 November 2009)
Threshers future in doubt as owner First Quench enters administration (30 October 2009)