According to the Brazil international's agent, Roger Wittmann, staying in the Bundesliga is an attractive proposition, but interest from the Premier League will also be difficult to turn down.
Gunners boss Arsene Wenger is believed to be an admirer of Gustavo's, and has been heavily linked with a move to bring him to the Emirates Stadium.
Meanwhile, Jose Mourinho has also been credited with an interest in the Bayern Munich star's services, so Chelsea could make a rival bid to lure him to Stamford Bridge.
Only last week, Gustavo admitted that he could leave the Allianz Arena before the close of the transfer window, following the arrivals of Mario Gotze and Thiago Alcantara under new manager Pep Guardiola.
The transfer developments have offered both Arsenal and Chelsea encouragement in their respective pursuits of the South American schemer, although rival interest from Wolfsburg could force one of their hands to steal a march on other suitors.
"If Bayern allows, Luiz will talk with every major and reputable club," confirmed Wittman in an interview with Kicker. "This includes VFL Wolfsburg."
The Daily Express understands that Gustavo will be available for as little as £15million, despite the fact he is under contract at Bayern Munich until June 2015.