Brunner's time back in the Swiss League could be temporary, and Zug GM Jakub Horak told the paper the team isn't banking on him, though they'd welcome him.
EV Zug could sign the 27-year-old to a "game-by-game agreement," the paper suggests, which would allow for an out-clause should an NHL team come calling with an acceptable offer.
Brunner, who spent almost five seasons with Zug, registered 12 goals and 14 assists for 26 points in 44 games with the Detroit Red Wings last season, his first in the NHL.
The native of Zurich, Switzerland, has received plenty of interest from NHL teams, but many are battling salary cap issues. The paper suggests a return to Detroit might be in the cards, but the Red Wings are among the teams with cap restraints.