The Portuguese veteran sustained a calf injury in last month’s Old Firm clash and couldn’t continue, and Alves wasn’t part of the Rangers squad that travelled to the Sunshine State at the weekend.
Graeme Murty confirmed Alves - who is targeting a place in his country’s World Cup squad this summer - would remain in his homeland for treatment.
“He is staying in Portugal,” Murty said, adding: “He has a significant problem or disruption with his calf so he won’t be in America. He will receive treatment in Portugal.
“I have no real timescale on how long he might be out for. I will have a closer brief with our medical staff over the coming days.”
The defender’s Ibrox future was thrown into doubt last month, when the 36-year-old hinted at a departure in order to boost his Russia 2018 hopes.
Describing himself as an ‘ambitious person’, he said: “I like to play, I don’t want to be a problem to anybody, I want to be a solution. If I don’t play so much then I need to think about [what happens in January].”
The Euro 2016 winner has been hampered by injury and Murty’s preference to play Danny Wilson and Ross McCrorie in central defence, and knows that this year’s World Cup will likely be his last major tournament.
“I am still playing for the national team - we have a World Cup soon and I need to play and be fit, to try to be there. This is important for me. Not just to help Rangers; I also want to help myself go to the World Cup.”