Stubbs told talkSPORT: "He's into the last six months of his contract and that's probably why there is speculation. He hasn't signed his contract yet, which he's not in a rush to do.
"He's got a fantastic relationship with the chairman. He's under no pressure from the chairman and the chairman has just probably said to him, 'the contract is there, when you're ready to speak, we'll speak', and the gaffer is comfortable with that at the moment.
"He probably doesn't want that to become a big issue and I know people will say the longer he takes to sign it, it does become an issue, but when the time is right I'm sure David Moyes will sit down with the chairman and say, 'come on, let's get it done'.
"This contract won't be about money for David Moyes. The money is just security, it's not about satisfaction. He doesn't take any pleasure about taking 'x' amount of money home a week.
"It's about the football, it's about the results, it's about success and it's about him proving himself as a manager. That's what he is looking for. It's about David Moyes becoming a better manager."