Gordon Sprenger, the chairman of the orchestra’s board, confirms that “conversations are occurring.”

This week’s concerts, from Thursday through Saturday, celebrate the Grammy awarded to Mr. Vanska and the orchestra in January for a recording of Sibelius’s First and Fourth Symphonies. This is Mr. Vanska’s first official appearance with the orchestra since July 2012, two months before management imposed a lockout of the players for their failure to agree to a draconian new contract. The dispute was to drag on for 16 rancorous months. (Mr. Vanska also conducted a concert in February 2013, celebrating a Grammy nomination for a recording of Sibelius’s Second and Fifth Symphonies, but that was organized by the players themselves.)

Since the players agreed to a contract with mollifying terms in January, there has been considerable public outcry for Mr. Vanska’s return as music director. And the announcement last week that Michael Henson, the orchestra’s embattled president and chief executive, whose ouster Mr. Vanska publicly advocated, will leave in August, seemed to clear the way for that return. (Mr. Henson’s announcement followed the departure of the former chairman of the board, Jon Campbell, concurrent with the contract settlement in January.)

There have been reports of divisions among board members, with some still angry over the ultimatum Mr. Vanska laid down last year, saying that the players would have to be back in action by September, to prepare adequately for the fall season, including two concerts at Carnegie Hall, or he would resign. He resigned. There is also residual anger over those incendiary informal remarks about Mr. Henson, which, however privately they may have been intended, quickly went public. Some on the board are said to be suggesting a position like principal conductor, widespread in Europe, which dispenses with the administrative duties typical of an American music directorship. Others are said to oppose Mr. Vanska’s return in any capacity.

Considerable urgency attaches to the situation, since this is the time of year when most major orchestras announce their next seasons, and when the Minnesota Orchestra would ordinarily be doing so. Gwen Pappas, the orchestra’s spokeswoman, said that a draft of the 2014-15 programs exists, obviously laced with uncertainties.