The 35-year-old has dropped into the free agent pool following his release by Birmingham City.
Elliott spent the second-half of the 2013/14 campaign on loan in Sky Bet League One at Bristol City.
Yeovil will be competing at that level next season and will be looking to add experience to their ranks.
Johnson has, however, revealed that Elliott is not among those in his thoughts.
He continues to play his transfer cards close to his chest, with those at Huish Park giving little away when it comes to recruitment plans.
Johnson told the Western Gazette on Elliott: "No, we're not interested. He played at Bristol City and I think if anybody was going to take him that would be Bristol City.
"Someone may have thrown us in to help whatever the situation is, I don't know.
"I'm not going to discuss any rumours throughout the summer, which is what people should expect because the minute I say 'yes' to a name, it may alert other teams.
"Unfortunately, nobody will be getting a lot out of me until the early part of pre-season."