Paraguay's medical staff are due to visit Santa Cruz to assess the seriousness of a knee tendon problem which has forced him to miss Blackburn's last two matches and will keep him out of Saturday's clash with West Ham.
"We will obviously tell them he is not capable of travelling," Allardyce said. "They are due to pay a visit, and we will have the discussion, but Roque is not fit to play any game of football until, at the very, very earliest, against Tottenham [on April 4]. It could be beyond that, so I can't see him going to Paraguay because he is not capable of playing."
Allardyce dismissed suggestions that Santa Cruz, who is expected to move to Manchester City at the end of the season and reunite with former Rovers manager Mark Hughes, may have played his last game for Blackburn.
"I think he'll be back this season," Allardyce said. "He is responding to treatment, but a lot slower than we expected. He is a talented player, we all know that, but I've managed without him before as he was injured when I arrived."