The 34-year-old's one-year deal with the Edinburgh club expired at the end of the season, but Maybury is keen to stay at Easter Road and continue working under manager Pat Fenlon in the next campaign.
A nomadic career has included spells with Leeds, Leicester and St Johnstone, but the Republic of Ireland international's longest stay was with over 100 games for Hibs' cross-city rivals Hearts.
"There is nothing definite at the moment so I am a bit in limbo," admitted Maybury.
"But my agent has spoken to Pat a couple of times while I spoke to the manager last week and we are keen to get something sorted.
"There is a lot going on so it is a case of being patient. However, I am hopeful we'll get something sorted out.
"I'm used to it at this stage of my career. I have had one-year contracts for the past few years, so you can't get too panicked.
"The hope is that I will be back in with Hibs come the new season."