Jenkins has played second fiddle to Andrew Sheridan since joining Toulon in the summer but he is determined to make a statement of his intentions by roaring against the Pumas.
"Every player who is involved with the four Home Nations has Lions ambitions and I am no different," said Jenkins.
"Even guys out in France who are not playing with England all want that carrot of playing for the Lions in the end.
"I have been involved with two tours and they are the pinnacle of your career, so I would like to be involved again.
"You always have a point to prove when you put the Welsh jersey on. I certainly would have not taken my place for granted during this series.
"I know there are people putting pressure on me. Paul James has been playing well in England and Ryan Bevington has been starting regularly for the Ospreys, so I am happy the coaches have shown faith in me.
"I have not started as many games in France as I would have liked, but on the positive side I have still been involved in 15 matches with Toulon. I am fresh and raring to go and get stuck in for my country again."
But Jenkins is well aware of the threat posed by Argentina, especially following their involvement in the inaugural Rugby Championship.
"They have had the first experience of playing in a major tournament outside the World Cup," added Jenkins.
"They will have had a good build-up and time together and know each other a lot better.
"Every time we play Argentina we know they are going to pose a strong forward challenge and a lot of their players are now in France."