Hummels was left out of the Germany side which beat Israel 2-0 in their last warm-up match, but Dortmund's director of sport Michael Zorc urged Low to put him in the team.
"The national coach should know that he can count on our players," Zorc told Kicker magazine.
"Hummels is Germany's best central defender."
The 23-year-old signed a new five-year contract with the Bundesliga champions on Sunday and he also has the backing of former Germany international Gunter Netzer.
"For me, (Arsenal defender) Per Mertesacker is the biggest question mark," said Germany's 1974 World Cup winner in the Bild newspaper.
"I would say that the Dortmund defender is more suited to partner Holger Badstuber in the centre of the defence.
"Mertesacker has yet to prove that he is in better form than Hummels."
What Mertesacker does have is a wealth of international experience and that is important to Low.
"Dortmund's players are very, very strong domestically and they are on the rise, but they are not as tried and tested internationally as the Bayern players," he said.
"There is a different level at a European Championships. With all due respect, we are not playing against Hoffenheim and Nurnberg.
"We are playing against the top 10 teams in the world - against Spain, the current world and European champions. That is the highest level."
The Arsenal defender could therefore have the edge, as do the contingent of eight Bayern Munich players, seven of whom lined up to face Israel last week.
Bastian Schweinsteiger was the only Bayern man not to feature in that game, but he appears to be winning his battle against a calf injury, leaving Mertesacker and Real Madrid duo Sami Khedira and Mesut Ozil as the only non-Bayern players currently making up Low's first-choice XI.