But the former England under-21 player has failed to win a senior English call so new Wales boss Speed is weighing up a fresh approach for playmaker Jones.
"It is important we look at all options," Speed told BBC Sport.
The Welsh squad boast talented midfielders such as Premier League trio Aaron Ramsey, Jack Collison and Dave Edwards plus Joe Ledley of Glasgow Celtic.
Tottenham Hotspur left-winger Gareth Bale is one of the form players of the Premier League while Leicester City's Andy King and Joe Allen of Swansea City are performing well in the Championship.
While Speed has also asked Fulham midfielder Simon Davies to reconsider his decision to retire from international football.
But Wales' new manager, a former esteemed top-flight midfielder himself, hopes to add further strength to the Welsh engine room.
Jones was approached by the Football Association of Wales when he was a teenager at Manchester United during Mark Hughes' tenure.
The Southport-born player had revealed Wales and United legend Ryan Giggs has tried to persuade him to play for Wales.
But Jones, who qualifies for Wales due to his North Wales-born father, wanted to wait to see if he had an international future with England as he 'considered himself an Englishman.'
Now, though, Speed may ask if Jones - Wolves team-mates of Wales pair Wayne Hennessey and David Edwards - of if he wants a second chance of an international future with Wales.
"I'd would consider asking him to play for Wales," Speed confirmed.
"I know Dave was asked a few years ago about his availability and he wanted to keep his options open.
"We have two players at Wolves already so I'm sure we can try and chat to him.
"It is a very personal and big decision in his career. But I'm sure we'll be exploring all of the avenues."
Jones' one England's under-21 cap was coming on as a substitute in a 2-2 draw in Sweden in March 2004
But Jones failed to break into the United first-team squad and left Old Trafford in 2007 in a £1m deal for Derby County.
He, however, failed to hold down a first-team place at Pride Park and joined Wolves in June 2008 for a reported £1.2m.
Jones, a regular in his first season at Molineux, has scored once in his nine starts for Wolves in the Premier League this season.
Source: BBC Sport
Source: BBC Sport