Rodriguez's agent Fabio Parisi said negotiations were delayed by Wolfsburg's participation in the Bundesliga play-offs, with the club securing survival on Monday thanks to a 2-0 aggregate win against Eintracht Braunschweig.
The Switzerland international has only played once since March due to injury but Parisi indicated a move to San Siro could be imminent for his client.
"The negotiations are continuing, it's just Wolfsburg were tied up with the relegation play-offs," Parisi told Radio24.
"The basic details are sorted out, we go forward and there's a very good chance it will go through.
"Everyone wants to finalise the move, the player wants to join Milan and Milan want to sign him.
"We just had to wait for the Wolfsburg result. I really think the move will be completed."
Milan, who completed the signing of defender Mateo Musacchio from Villarreal and extended the contract of coach Vincenzo Montella on Tuesday, finished sixth in Serie A and qualified for the Europa League as a result.
After an April takeover, the club's new owners, Rossoneri Sport Investment Lux - owned by Chinese businessman Yonghong Li - are expected to spend heavily to improve Montella's squad, although they have a battle to hold on to their in-demand teenage goalkeeper Gianluigi Donnarumma, who is entering the last year of his contract.
Milan are also in talks to sign winger Rachid Ghezzal, whose Lyon contract is set to expire.
Agent Abdelkader Ghezzal told Mediaset Premium: "Milan are interested in my brother Rachid.
"There was already a meeting a while ago. The door is always open, we'll see how this pans out."