Jones, the last Australian to win the Formula 1 title, believes that Webber would find himself revitalised by an opportunity to race for the Maranello team.
Speaking in a podcast put together by the Australian Grand Prix organisers, Jones said: "Mark has already done one of the two things that most Formula 1 drivers would like to do, and that's win Monaco. The other one is to drive for Ferrari.
"I'm sure he'd have a look at it. If he goes to Ferrari, it could be a breath of fresh air - it's very prestigious and something really good to have on your CV. He gets on extremely well with [Fernando] Alonso, so maybe that could be a good way for him to go."
Webber's contract with Red Bull runs out at the end of this season, and his strong form in the opening part of this campaign has again ignited speculation that he is on Ferrari's radar as a potential replacement for Felipe Massa.
Although going up alongside Alonso would not be an easy thing to do, Jones reckons that Webber already faces a big challenge at Red Bull with Sebastian Vettel.
He added: "Personally, I think that Mark is with a good team (but) having said that, if he signed on with Red Bull next year he's still going to have Vettel as his team-mate, which is a pretty hard task."