The Switzerland international is a key part of the Bundesliga side, and is their first choice left-back.
He has scored an impressive 10 goals in 34 games this season, as well as contributing five assists.
This summer Wolfsburg hold the cards regarding the 22-year-old, but BILD report that from 2016, a release clause of €30 million can be activated.
That is a high price for a left-back, but Rodriguez could be worth it, regarded as one the best players in his position in European football.
Already with 29 caps to his name for Switzerland, Rodriguez featured at the 2014 World Cup, and has 17 goals and 21 assists in total for Wolfsburg to his name; impressive figures for a defender of his age.
Arsenal may have a need opening up at left-back, with TalkSport reporting Nacho Monreal remains a target for Spanish side Athletic Bilbao, who are expected to revisit their interest this summer.
The question is whether their interest is decisive enough they act now, and risk having the price dictated by Wolfsburg who could look to sell him for higher than his release clause while they can, or hold onto Monreal for one more year and seek to pay up the fixed fee for the Swiss star in 12 months time.
If they choose not to pursue him this summer, Arsenal fans could get a close look at him any way, with Wolfsburg named as one of the three visiting clubs for the annual Emirates Cup.