But the centre is expected to make his return in the GUINNESS PRO12 this weekend when Edinburgh visit Rodney Parade.
Morgan's return comes at a crucial junction for Jones with the Dragons currently sitting tenth in the GUINNESS PRO12 with five games remaining.
And Jones is confident that a run of games will see Morgan develop into a regular at international level and is keen to see him challenge Jonathan Davies for a spot in Warren Gatland's starting XV.
"Tyler is desperate for a run of games and we sincerely hope that he can start that on Sunday against Edinburgh," said Jones.
"I think it's important for him - he's 50 games away from becoming the standard of player he wants to be.
"And in those 50 games he's got a lot of errors to make and a lot of rugby to play.
"How nice would it be that he could go down to New Zealand and to challenge Jonathan Davies for that 13 shirt.
"And that's what the national selectors will be looking for. We've all seen the potential with Tyler.
"His last game of rugby was against South Africa and he did really well that day."
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