Both United and Chelsea are looking to strengthen the position this summer, with Ashley Cole and Patrice Evra out of contract.
Rodriguez, 21, has been one of the surprise stars of the Bundesliga season so far. And Wolfsburg general manager Klaus Allofs wants to get the left-back signed up to another long-term contract.
"Ricardo Rodriguez is a first-team regular of our club," he told Kicker-Sportmagazin.
"We are very happy with the progress and performances of Ricardo. We would definitely like him to sign a new deal."
Rodriguez, who joined Wolfsburg from Swiss side FC Zurich, has a contract with the Bundesliga side until the summer of 2016.
The Swiss international is set to go to the World Cup this summer, but a couple of impressive performances in Brazil and Wolfsburg could face a real fight to keep hold of him.
Manchester United face Norwich in the Premier League this weekend, while Chelsea travel to Liverpool.