Assistant manager Ian Hendon told BBC Radio Kent: "Its now down to the manager and the chairman to sit down and sort that out.
"We'd obviously like to keep Danny - he's done great for us."
Hendon continued: "He's a good pro and works his socks off so I'm sure that will be sorted out in the very near future.
"It's just a matter of the manager and the chairman sitting down and having a chat.
"We've said we'd like to keep Danny - and now it's up to the powers that be."
Spiller began his career as a trainee with the Gills and made his senior debut for them in 2001.
He moved to Millwall on a free transfer in 2007 but a series of injuries prevented his progress at the New Den.
During the 2009/10 season, he had spells at Wycombe, Welling United and Dagenham & Redbridge.