Griffiths impressed despite Dragons' 21-16 Pro12 defeat by Scarlets at the Principality Stadium.
Wales face Tonga and Samoa in June and Jones believes it will be the perfect opportunity for Griffiths to gain international experience.
"I'd like to think they'll have a look at him," Jones said.
"Justin Tipuric and Sam Warburton I think will go with the Lions so there is an opportunity for him.
"There's lot of good young number sevens. James Davies is an excellent player as well and has a massive influence on the game for the Scarlets.
"Ellis Jenkins has been there and has got a bit of experience. Maybe there's a chance to look at Oliver with Ellis or with James."
Jones described 22-year-old Griffiths as the "complete open-side flanker"
"He's got something special. He's got leadership qualities and is very mature for a young kid of 21," he added.
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"He needs to perform at that level consistently and the thing that's going to help him get into the Welsh squad is the team being successful.
"When this team is fourth in the league there will be a lot of players going with the national team but ultimately we need to be more consistent.
Jones was left frustrated despite his side picking up a losing bonus point in the Judgement Day defeat by Scarlets.
"Losing is not acceptable and it's not great but ultimately I couldn't have asked for much more I felt," Jones said.
"I'm proud of the players. They followed the game plan, our lineout game was good and we defended well against a very good Scarlets team.
"There was a period which broke our spirit a little bit with [Adam Hughes'] yellow card and a couple of decisions went against us and we failed to deal with that.
"The scrum was the difference and losing [prop] Lloyd Fairbrother was a disappointment early in the game and it was always going to be a challenge against a good Scarlets scrum.
"But the way we came back at the end is the most promising thing and we scored and excellent try which I think we deserved."
Dragons are away to Edinburgh in their next game on Friday, 28 April and host Cardiff Blues in the final game of the season on 6 May.
Former Wales captain Jones says the target is to finish the season above Edinburgh, who are currently one place above them in ninth spot.
"It's been a tough season and hasn't been a great season, we know that," Jones added.
"We've been 10th for many years and there's an opportunity still to finish ninth.
"Edinburgh are in the same boat as us and we've got to go there believing we can win and we fancy our chances against the Blues.
"We've got to bring that application, intensity and belief and that's the challenge for this group and if we do that we've got a chance of turning this season into finishing ninth."
Newport Gwent Dragons head coach Kingsley Jones says flanker Ollie Griffiths has a "very good chance" of being picked by Wales.