Boateng was injured midway through their 2-1 Bundesliga victory at Hamburg SV and is suspected to have suffered a serious adductor muscle injury that could put his Euro 2016 participation in doubt.
"We will support him," Germany coach Loew told reporters in Munich on Monday.
"I talked to Jerome here in Munich and I told him I believe he can jump on the Euro train despite this serious injury.
"Just as I did for (midfielder) Sami Khedira for the 2014 World Cup, I will keep the door open as long as possible for Jerome. He is a fighter by nature and is professional."
Germany have been drawn the Euro 2016 Group C along with Poland, Northern Ireland and Ukraine, with their first game on June 12.
The 27-year-old Boateng, a 2014 World Cup winner, has won 57 caps for Germany.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
