Veteran midfielder Oakley was not offered fresh terms at the end of last season due to the club's delicate financial situation but Tisdale has always stressed his desire to try and hang on to the 35-year-old.
Defender Tully, meanwhile, was one of a handful of players offered a new deal although he is yet to sign and the offer has had to be put to one side for the time being, with Tisdale now unsure whether the required funds are still available for the right-back.
The Grecians boss told the club's official website: "Matt Oakley hasn't signed yet, but he's come back to training and he wants to play for us. We've been very transparent over the last month or two that we'd like to sign him and we'll try to find a way.
"In very tough times, the club have been doing all they can to make it possible for me - so I'm hoping that will get done."
Regarding Tully, he added: "The club is doing everything they can to make funds available for me, but there's no guarantee that I'll be able to make that signing.
"Steve was in training with us Monday and he's not yet signed elsewhere, so it'd be great if I could keep hold of him - but that's the way things are. It's a 'wait and see' on that one, but there's no guarantee that I'm going to be able to do it."
Meanwhile, highly-regarded midfielder David Wheeler has joined Exeter on trial from non-league Staines this week with the hope of impressing Tisdale.