"It is my understanding that we will have the player in Munich by July 1," Hoeness told reporters on Monday.
"We have agreed with the player but not yet with Zenit on the date. There are still some question marks regarding whether he will come in April or July."
Tymoschuk, 29, was targeted by the Bavarian giants since the end of last season, which saw him helping Zenit to an impressive UEFA Cup title.
The Ukraine international's arrival was intended to cover for unsettled Dutchman Mark van Bommel, who was on brink of leaving Allianz Arena.
However, Hoeness implied that the 31-year-old, who will run out of contract in the summer, could finally extend his stay with Bayern.
"I personally continue to believe we’ll succeed in keeping Mark here in Munich. That’s what we’ve always been aiming for, and I’ve heard no suggestion it’s not possible," Hoeness said.