The Dutch teenager has been allowed to continue his six-month loan spell at Scottish Premier League side, Falkirk.
Given is expected to be back in action before the end of the month but, with the Irishman having suffered two previous groin problems last season, Allardyce is considering signing a third goalkeeper regardless of his rate of recovery.
"We have a three-week window to find someone else if I think I need to," said the United boss.
"I'm sure Shay will be fine in two or three weeks, but from thereon if there's another problem with one of the goalkeepers, I have to make a decision as to whether or not I go out and buy one.
"Tim Krul isn't an option. I've spoken to the staff and the consensus is that he's too inexperienced and too young.
"He has great potential but he needs more experience playing first-team football at a lesser club. That's better than bringing him here and putting him into a situation he's not capable of coping with."
Albert Luque's father and agent, Rafael, claims that his son is on the verge of completing a loan move to Spanish side Levante.
The Valencia-based club are understood to be keen on striking a season-loan agreement for Luque, who has failed to impress since making a £9.5m move from Deportivo La Coruna in 2005.
"I believe that we will soon be in Valencia," said Luque senior. "I have attended some meetings this week and I expect a solution."
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