Jones' Ospreys team-mate, scrum-half Rhys Webb, became the latest player to agree a new dual deal on Wednesday.
"I'd like to think that Alun Wyn will sign but that's not settled as yet," Davies told BBC Radio Wales.
"We'll wait and see really. Ospreys and the Welsh Rugby Union, along with Alun and his advisors, are in discussion."
Wales lock Jones, 30, whose current deal expires at the end of the season, said he was "weighing up" his options in November.
Dual contracts are 60% funded by the WRU and 40% by the regions.
Davies believes there are additional benefits to the dual contracts for the players involved.
"It's more than just playing in Wales and playing for the national team as well," he added.
"I think some of the leading players understand they are looked after pretty well by Warren Gatland and his coaching staff, in terms of the amount of games they play and the conditioning they receive.
"So I think there's a bigger picture than just playing for the Ospreys and just playing for Wales - there are other things to take into consideration as well."
Negotiations over a new national dual contract for Ospreys' Alun Wyn Jones remain ongoing, says Welsh Rugby Union (WRU) chairman Gareth Davies.