Germany's Neuer 'a while' away from full fitness
Neuer hurt his right shoulder in Bayern Munich's 2-0 DFB Pokal win over Borussia Dortmund on May 17.
The shot-stopper remains a concern for Low, who looks set to regain Philipp Lahm and Bastian Schweinsteiger for training in the coming days.
"We have to decide day by day how it is going on. I think it is positive that both (Lahm, Schweinsteiger) are back on the field and we are very confident," Germany team manager Oliver Bierhoff said.
"For Manuel it will certainly take a while until his shoulder is fine again and I don't think that will be here in South Tyrol.
"Philipp and Bastian need to give us daily feedback after every training session how they feel and I think they will soon be back again in the squad session."
Real Madrid midfielder Sami Khedira joined up with the squad on Monday, having helped the La Liga side win the UEFA Champions League just days prior.
Bierhoff said it was Khedira's choice not to take a break after his domestic season finished, with the 27-year-old battling a cold on arrival.
"He was warmly welcomed and everyone was happy he arrived as a winner," Bierhoff said.
"He was a little ailing because of a cold, but the most important thing is that he is physically all right.
"I didn't talk to the coach, I don't think he will play with the team today, but he is able to play and it was him who said he wants to come straight here after the Champions League final.
"He knows that there is still some work to do, that he needs to be very disciplined and I think that he will do that with us."