Former Fulham player Baird can sign for a club after the transfer deadline as he is a free agent, but Redknapp does not want to wait too long for an answer.
"He's still here training with us," said Redknapp of the 31-year-old.
"We've made him an offer and it's up to Chris really whether he wants to take it.
"I think we need to know pretty soon. He can sign after the deadline because he's out of work, but we need an answer."