The England midfielder joined the south coast club on the final day of the window in one of the most surprising deals of the summer.
Speaking at Soccerex Global Convention in Manchester, Mostyn said: “I think anything is possible.
The best we can do is integrate Jack into the team and help him fulfil what he wants. Whether or not we will go beyond a season, I think everything is possible.
"You have to be realistic and Jack may well consider his home to be back at Arsenal. If that was the case then we couldn't disagree with his decision - and the decision will be his.
"But if there is a possibility and Eddie Howe decides that he's somebody he wants to keep it will be up to him. He will have to persuade [owner] Maxim Demin to unload a huge treasure chest in order to keep him.
"That would be the $64m question - it may even be the £64m transfer fee!"